Numerical and Analytical Methods for Variational Inequalities and Related Problems with Applications

1 Department of Mathematics, Nanjing University, Nanjing 210093, China 2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA 3 Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan 4 Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan 5 School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

[1]  Rudong Chen,et al.  A general iterative method for an infinite family of nonexpansive mappings , 2008 .

[2]  Muhammad Aslam Noor,et al.  Some new unified iteration schemes with errors for nonexpansive mappings and variational inequalities , 2007, Appl. Math. Comput..

[3]  M. Tian A general iterative algorithm for nonexpansive mappings in Hilbert spaces , 2010 .

[4]  Habtu Zegeye,et al.  On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces , 2009 .

[5]  M. Noor New approximation schemes for general variational inequalities , 2000 .

[6]  Yair Censor,et al.  The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space , 2011, J. Optim. Theory Appl..

[7]  Yeol Je Cho,et al.  On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces , 2010 .

[8]  M. Cojocaru Monotonicity and existence of periodic orbits for projected dynamical systems on Hilbert spaces , 2005 .

[9]  Jong Soo Jung Strong convergence of composite iterative methods for equilibrium problems and fixed point problems , 2009, Appl. Math. Comput..

[10]  Y. Cho,et al.  A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings , 2007 .

[11]  Nan-jing Huang,et al.  The generalized f-projection operator and set-valued variational inequalities in Banach spaces☆ , 2009 .

[12]  Poom Kumam,et al.  Strong Convergence Theorems for Countable Families of Uniformly Quasi--Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems , 2011 .

[13]  A. N. Tikhonov,et al.  On the stability of the functional optimization problem , 1966 .

[14]  Muhammad Aslam Noor,et al.  Quartic splines solutions of third-order obstacle problems , 2004, Appl. Math. Comput..

[15]  Satit Saejung,et al.  Strong Convergence to Common Fixed Points of Countable Relatively Quasi-Nonexpansive Mappings , 2008 .

[16]  Rabian Wangkeeree,et al.  A GENERAL ITERATIVE SCHEME FOR STRICT PSEUDONONSPREADING MAPPING RELATED TO OPTIMIZATION PROBLEM IN HILBERT SPACES , 2011 .

[17]  Muhammad Aslam Noor,et al.  Cubic splines method for a system of third-order boundary value problems , 2003, Appl. Math. Comput..

[18]  M. Noor,et al.  Some aspects of variational inequalities , 1993 .

[19]  Franco Giannessi,et al.  Regularization of non-coercive quasi variational inequalities , 2000 .

[20]  Tomonari Suzuki Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals , 2005 .

[21]  W. Oettli,et al.  From optimization and variational inequalities to equilibrium problems , 1994 .

[22]  Y. Xia,et al.  Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems , 2004 .

[23]  Y. Alber Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications , 1993, funct-an/9311001.

[24]  Poom Kumam,et al.  Existence and convergence theorems for the new system of generalized mixed variational inequalities in Banach spaces , 2012 .

[25]  H. Mönch,et al.  Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces , 1980 .

[26]  Ahmed Alsaedi,et al.  Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions , 2011 .

[27]  谷峰 CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS , 2006 .

[28]  Poom Kumam,et al.  A modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in Banach spaces , 2011, Comput. Math. Appl..

[29]  Jinlu Li The generalized projection operator on reflexive Banach spaces and its applications , 2005 .

[30]  A. Hoffman On approximate solutions of systems of linear inequalities , 1952 .

[31]  Eisa A. Al-Said Numerical solutions for system of third-order boundary value problems , 2001, Int. J. Comput. Math..

[32]  Jen-Chih Yao,et al.  Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems , 2008, J. Glob. Optim..

[33]  Jong-Shi Pang,et al.  A Posteriori Error Bounds for the Linearly-Constrained Variational Inequality Problem , 1987, Math. Oper. Res..

[34]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[35]  K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[36]  Hong-Kun Xu An Iterative Approach to Quadratic Optimization , 2003 .

[37]  F. Browder,et al.  NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[38]  A. Nagurney,et al.  On the stability of projected dynamical systems , 1995 .

[39]  Liu Liu,et al.  Projection algorithms for the system of mixed variational inequalities in Banach spaces , 2011, Math. Comput. Model..

[40]  N. Xiu,et al.  Global Projection-Type Error Bounds for General Variational Inequalities , 2002 .

[41]  M. Beatrice Lignola,et al.  Well-posedness for Optimization Problems with Constraints defined by Variational Inequalities having a unique solution , 2000, J. Glob. Optim..

[42]  Zhenhai Liu,et al.  Browder-Tikhonov regularization of non-coercive evolution hemivariational inequalities , 2005 .

[43]  B. Piatek,et al.  Best approximation of coincidence points in metric trees , 2008 .

[44]  E. Tarafdar,et al.  FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS OF NONEXPANSIVE TYPE , 1980 .

[45]  Narin Petrot,et al.  A resolvent operator technique for approximate solving of generalized system mixed variational inequality and fixed point problems , 2010, Appl. Math. Lett..

[46]  Jing Fang Tan,et al.  A New Hybrid Algorithm for Solving a System of Generalized Mixed Equilibrium Problems, Solving a Family of Quasi-ϕ-Asymptotically Nonexpansive Mappings, and Obtaining Common Fixed Points in Banach Space , 2011, Int. J. Math. Math. Sci..

[47]  B. Pettis On integration in vector spaces , 1938 .

[48]  A. Moudafi Viscosity Approximation Methods for Fixed-Points Problems , 2000 .

[49]  Giuseppe Marino,et al.  A general iterative method for nonexpansive mappings in Hilbert spaces , 2006 .

[50]  Jack Markin,et al.  Fixed points, selections and best approximation for multivalued mappings in R-trees , 2007 .

[51]  Yair Censor,et al.  A multiprojection algorithm using Bregman projections in a product space , 1994, Numerical Algorithms.

[52]  Bashir Ahmad,et al.  Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations , 2009 .

[53]  S. Szufla,et al.  On the application of measure of noncompactness to existence theorems , 1986 .

[54]  Nan-Jing Huang,et al.  Generalized quasi-variational-like hemivariational inequalities , 2008 .

[55]  Yeol Je Cho,et al.  Iterative algorithms for hierarchical fixed points problems and variational inequalities , 2010, Math. Comput. Model..

[56]  Anna Nagurney,et al.  Dynamical systems and variational inequalities , 1993, Ann. Oper. Res..

[57]  Hai-Wei Sun,et al.  A high‐order compact boundary value method for solving one‐dimensional heat equations , 2003 .

[58]  Meijuan Shang,et al.  Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings , 2007 .

[59]  Suthep Suantai,et al.  A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings , 2009 .

[60]  Lu-Chuan Zeng,et al.  STRONG CONVERGENCE THEOREM BY AN EXTRAGRADIENT METHOD FOR FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS , 2006 .

[61]  Wataru Takahashi,et al.  Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings , 2003 .

[62]  William A. Kirk,et al.  Fixed point theorems in R-trees with applications to graph theory , 2006 .

[63]  V. Lakshmikantham,et al.  Nonlinear Integral Equations in Abstract Spaces , 1996 .

[64]  Hong-Kun Xu,et al.  Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications , 2011 .

[65]  Poom Kumam,et al.  Strong Convergence Theorems of Modified Ishikawa Iterations for Countable Hemi-Relatively Nonexpansive Mappings in a Banach Space , 2009 .

[66]  Wen-Xue Zhou,et al.  Weak Solutions for Nonlinear Fractional Differential Equations in Banach Spaces , 2012 .

[67]  Idris Dag,et al.  A numerical solution of the Burgers' equation using cubic B-splines , 2005, Appl. Math. Comput..

[68]  C. Byrne,et al.  A unified treatment of some iterative algorithms in signal processing and image reconstruction , 2003 .

[69]  M. Noor General variational inequalities , 1988 .

[70]  Feng Gao,et al.  Solving third-order obstacle problems with quartic B-splines , 2006, Appl. Math. Comput..

[71]  Jun Wang,et al.  On the Stability of Globally Projected Dynamical Systems , 2000 .

[72]  Muhammad Aslam Noor,et al.  Numerical solutions of third-order obstacle problems , 1998, Int. J. Comput. Math..

[73]  Hong-Kun Xu,et al.  Remarks on multivalued nonexpansive mappings , 1995 .

[74]  Hong Cao,et al.  Static and dynamic analysis of straight bars with variable cross-section , 1996 .

[75]  Rong Hu,et al.  Parametric well-posedness for variational inequalities defined by bifunctions , 2007, Comput. Math. Appl..

[76]  W. A. Kirk,et al.  Topics in Metric Fixed Point Theory , 1990 .

[77]  Jen-Chih Yao,et al.  Well-posedness by perturbations of mixed variational inequalities in Banach spaces , 2010, Eur. J. Oper. Res..

[78]  Yi-bin Xiao,et al.  Well-posedness of Hemivariational Inequalities and Inclusion Problems , 2011 .

[79]  Johnny Henderson,et al.  Impulsive differential inclusions with fractional order , 2010, Comput. Math. Appl..

[80]  P. Maingé Strong Convergence of Projected Subgradient Methods for Nonsmooth and Nonstrictly Convex Minimization , 2008 .

[81]  S. Reich Weak convergence theorems for nonexpansive mappings in Banach spaces , 1979 .

[82]  Jacqueline Morgan,et al.  Approximate Solutions and α-Well-Posedness for Variational Inequalities and Nash Equilibria , 2002 .

[83]  Teck-Cheong Lim,et al.  On fixed point stability for set-valued contractive mappings with applications to generalized differential equations , 1985 .

[84]  Edward H. Twizell,et al.  Non polynomial spline approach to the solution of a system of third-order boundary-value problems , 2005, Appl. Math. Comput..

[85]  Syed Tauseef Mohyud-Din,et al.  Solutions of Nonlinear Differential Equations by Exp-function Method , 2009 .

[86]  Wataru Takahashi,et al.  Strong Convergence of a Proximal-Type Algorithm in a Banach Space , 2002, SIAM J. Optim..

[87]  C. F. Li,et al.  Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations , 2010, Comput. Math. Appl..

[88]  Troy L. Hicks,et al.  On the Mann iteration process in a Hilbert space , 1977 .

[89]  Jen-Chih Yao,et al.  Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities , 2008, Math. Methods Oper. Res..

[90]  P. Ánh A hybrid extragradient method extended to fixed point problems and equilibrium problems , 2013 .

[91]  Y. Censor,et al.  Iterations of paracontractions and firmaly nonexpansive operators with applications to feasibility and optimization , 1996 .

[92]  Jun Wang,et al.  A general projection neural network for solving monotone variational inequalities and related optimization problems , 2004, IEEE Transactions on Neural Networks.

[93]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[94]  Hong-Kun Xu,et al.  Iterative methods for strict pseudo-contractions in Hilbert spaces , 2007 .

[95]  Syed Tauseef Mohyud-Din,et al.  Numerical Solution of Modified Equal Width Wave Equation , 2010 .

[96]  Yi-bin Xiao,et al.  Sub–supersolution method and extremal solutions for higher order quasi-linear elliptic hemi-variational inequalities☆ , 2007 .

[97]  Suthep Suantai,et al.  Existence and stability of iterative algorithms for the system of nonlinear quasi-mixed equilibrium problems , 2011, Appl. Math. Lett..

[98]  S. Nadler Multi-valued contraction mappings. , 1969 .

[99]  Nan-Jing Huang,et al.  The generalised f -projection operator with an application , 2006 .

[100]  Muhammad Aslam Noor,et al.  On viscosity iterative methods for variational inequalities , 2007 .

[101]  Michael C. Ferris,et al.  Engineering and Economic Applications of Complementarity Problems , 1997, SIAM Rev..

[102]  Jen-Chih Yao,et al.  On modified iterative method for nonexpansive mappings and monotone mappings , 2007, Appl. Math. Comput..

[103]  Hong-Kun Xu Iterative Algorithms for Nonlinear Operators , 2002 .

[104]  Hong-Kun Xu,et al.  Averaged Mappings and the Gradient-Projection Algorithm , 2011, J. Optim. Theory Appl..

[105]  P. L. Combettes,et al.  Solving monotone inclusions via compositions of nonexpansive averaged operators , 2004 .

[106]  Tippawan Puttasontiphot,et al.  Mann and Ishikawa Iteration Schemes for Multivalued Mappings in CAT(0) Spaces , 2010 .

[107]  Muhammad Aslam Noor,et al.  An explicit projection method for a system of nonlinear variational inequalities with different (gamma, r)-cocoercive mappings , 2007, Appl. Math. Comput..

[108]  Jianghua Fan A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces , 2008 .

[109]  Li Qiusheng,et al.  Analysis of Free Vibrations of Tall Buildings , 1994 .

[110]  Poom Kumam,et al.  A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping , 2009 .

[111]  B. Ahmad,et al.  Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional or , 2011 .

[112]  A. Moudafi,et al.  Proximal and Dynamical Approaches to Equilibrium Problems , 1999 .

[113]  Robert L. Taylor,et al.  Self-adjoint differential equations , 2005 .

[114]  Hong-Kun Xu,et al.  Remarks on the Gradient-Projection Algorithm , 2011 .

[115]  T. Zolezzi Extended well-posedness of optimization problems , 1996 .

[116]  I. Yamada,et al.  Quadratic optimization of fixed points of nonexpansive mappings in Hilbert space , 1998 .

[117]  Jen-Chih Yao,et al.  An Extragradient Method for Fixed Point Problems and Variational Inequality Problems , 2007 .

[118]  Narin Petrot,et al.  System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications , 2011 .

[119]  I. Yamada,et al.  Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings , 1998 .

[120]  E. Kaufmann,et al.  Positive solutions of a boundary value problem for a nonlinear fractional differential equation. , 2008 .

[121]  Anna Ochal,et al.  Dynamic bilateral contact problem for viscoelastic piezoelectric materials with adhesion , 2008 .

[122]  Wataru Takahashi,et al.  Weak and Strong Convergence of Solutions to Accretive Operator Inclusions and Applications , 2000 .

[123]  Muhammad Aslam Noor,et al.  Some developments in general variational inequalities , 2004, Appl. Math. Comput..

[124]  R. Rockafellar On the maximality of sums of nonlinear monotone operators , 1970 .

[125]  Teck-Cheong Lim,et al.  A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space , 1974 .

[126]  F. Browder Nonlinear operators and nonlinear equations of evolution in Banach spaces , 1976 .

[127]  Muhammad Aslam Noor,et al.  Numerical solutions of third-order system of boundary value problems , 2007, Appl. Math. Comput..

[128]  W. A. Kirk Hyperconvexity of R-trees , 2007 .

[129]  Somyot Plubtieng,et al.  A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings , 2008, Appl. Math. Comput..

[130]  Jürgen Schu,et al.  Iterative construction of fixed points of asymptotically nonexpansive mappings , 1991 .

[131]  Yong Zhou,et al.  Existence of solutions for a class of fractional boundary value problems via critical point theory , 2011, Comput. Math. Appl..

[132]  R. U. Verma,et al.  Projection methods, algorithms, and a new system of nonlinear variational inequalities , 2001 .

[133]  T. Zolezzi,et al.  Well-posedness criteria in optimization with application to the calculus of variations , 1995 .

[134]  Koji Aoyama Halpern's Iteration for a Sequence of Quasinonexpansive Type Mappings , 2011, NL-MUA.

[135]  Hong-Kun Xu VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS , 2004 .

[136]  I. Yamada The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings , 2001 .

[137]  J. Diestel Geometry of Banach Spaces: Selected Topics , 1975 .

[138]  Nan-Jing Huang,et al.  Properties of the generalized f-projection operator and its applications in Banach spaces , 2007, Comput. Math. Appl..

[139]  Shi Sheng Zhang,et al.  Modified block iterative method for solving convex feasibility problem, equilibrium problems and variational inequality problems , 2012 .

[140]  Ireneusz Kubiaczyk,et al.  ON BOUNDED PSEUDO AND WEAK SOLUTIONS OF A NONLINEAR DIFFERENTIAL EQUATION IN BANACH SPACES , 1999 .

[141]  S. Banach Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

[142]  Dumitru Motreanu,et al.  Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities , 1998 .

[143]  Poom Kumam,et al.  Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi--Asymptotically Nonexpansive Mappings , 2010 .

[144]  Hikmet Caglar,et al.  The numerical solution of the one-dimensional heat equation by using third degree B-spline functions , 2008 .

[145]  Donal O'Regan,et al.  Fixed-point theory for weakly sequentially continuous mappings , 1998 .

[146]  Hussein A. H. Salem,et al.  A NOTE ON THE FRACTIONAL CALCULUS IN BANACH SPACES , 2005 .

[147]  E. O. Tuck,et al.  A Numerical and Asymptotic Study of Some Third-Order Ordinary Differential Equations Relevant to Draining and Coating Flows , 1990, SIAM Rev..

[148]  P. D. Panagiotopoulos,et al.  Nonconvex energy functions. Hemivariational inequalities and substationarity principles , 1983 .

[149]  Zhenhai Liu,et al.  Existence results for quasilinear parabolic hemivariational inequalities , 2008 .

[150]  S. Nadler,et al.  Multi-valued contraction mappings in generalized metric spaces , 1970 .

[151]  Fioravante Patrone,et al.  A characterization of tyhonov well-posedness for minimum problems, with applications to variational inequalities (∗) , 1981 .

[152]  Wataru Takahashi,et al.  APPROXIMATION OF SOLUTIONS OF VARIATIONAL INEQUALITIES FOR MONOTONE MAPPINGS , 2004 .

[153]  İdris Dağ,et al.  A CUBIC B-SPLINE COLLOCATION METHOD FOR THE EW EQUATION , 2004 .

[154]  Wataru Takahashi,et al.  Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings , 2006 .

[155]  William A. Kirk,et al.  A Fixed Point Theorem for Mappings which do not Increase Distances , 1965 .

[156]  G. Isac,et al.  Some solvability theorems for nonlinear equations with applications to projected dynamical systems , 2009 .

[157]  Lishan Liu,et al.  Ishikawa and Mann Iterative Process with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces , 1995 .

[158]  I. Ciorǎnescu Geometry of banach spaces, duality mappings, and nonlinear problems , 1990 .

[159]  Tomonari Suzuki,et al.  Moudafi's viscosity approximations with Meir–Keeler contractions , 2007 .

[160]  Yi-bin Xiao,et al.  Sub–super-solution method for a class of higher order evolution hemivariational inequalities ☆ , 2009 .

[161]  Poom Kumam,et al.  The shrinking projection method for solving generalized equilibrium problems and common fixed points for asymptotically quasi-ϕ-nonexpansive mappings , 2011 .

[162]  Habtu Zegeye,et al.  Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings , 2009 .

[163]  Poom Kumam,et al.  Convergence theorems of a hybrid algorithm for equilibrium problems , 2009 .

[164]  Shih-Sen Chang,et al.  On Chidume's Open Questions and Approximate Solutions of Multivalued Strongly Accretive Mapping Equations in Banach Spaces☆☆☆ , 1997 .

[165]  Liping Zhang A nonlinear complementarity model for supply chain network equilibrium , 2007 .

[166]  Muhammad Aslam Noor,et al.  Strong convergence of three-step relaxed hybrid steepest-descent methods for variational inequalities , 2008, Appl. Math. Comput..

[167]  William A. Kirk,et al.  A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS , 1972 .

[168]  Wataru Takahashi,et al.  Weak convergence of an iterative sequence for accretive operators in Banach spaces , 2006 .

[169]  Shih-Sen Chang,et al.  Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces , 2010 .

[170]  Wataru Takahashi,et al.  Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces , 2007 .

[171]  M. A. Noor,et al.  Finite-Difference Method for a System of Third-Order Boundary-Value Problems , 2002 .

[172]  G. Stampacchia,et al.  On the regularity of the solution of a variational inequality , 1969 .

[173]  Jen-Chih Yao,et al.  Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities , 2005 .

[174]  Nan-Jing Huang,et al.  Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations , 2011, J. Optim. Theory Appl..

[175]  Ya. I. Alber Generalized Projection Operators in Banach Spaces: Properties and Applications , 1993 .

[176]  X. X. Huang,et al.  Levitin–Polyak well-posedness of variational inequality problems with functional constraints , 2009, J. Glob. Optim..

[177]  Habtu Zegeye,et al.  Approximating common solution of variational inequality problems for two monotone mappings in Banach spaces , 2011, Optim. Lett..

[178]  Paul-Emile Maingé,et al.  The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces , 2010, Comput. Math. Appl..

[179]  Poom Kumam,et al.  A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping , 2008 .

[180]  A. Moudafi,et al.  SECOND-ORDER DIFFERENTIAL PROXIMAL METHODS FOR EQUILIBRIUM PROBLEMS , 2003 .

[181]  Józef Banaś,et al.  On some measures of noncompactness in the space of continuous functions , 2008 .

[182]  Donal O'Regan,et al.  WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES , 1999 .

[183]  Yeol Je Cho,et al.  Regularization and iterative method for general variational inequality problem in hilbert spaces , 2011 .

[184]  Juan J. Nieto,et al.  Some new existence results for fractional differential inclusions with boundary conditions , 2009, Math. Comput. Model..

[185]  Zhigang Hu,et al.  Boundary value problems for fractional differential equations , 2014, Boundary Value Problems.

[186]  Emmett B. Keeler,et al.  A theorem on contraction mappings , 1969 .

[187]  Liqun Qi,et al.  Global Error Bound for the Generalized Linear Complementarity Problem over a Polyhedral Cone , 2009, J. Optimization Theory and Applications.

[188]  Muhammad Aslam Noor,et al.  Extended general variational inequalities , 2009, Appl. Math. Lett..

[189]  Steven R. Dunbar Geometric analysis of a nonlinear boundary value problem from physical oceanography , 1993 .

[190]  Nan-Jing Huang,et al.  Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities , 2009, J. Glob. Optim..

[191]  Abdul Latif,et al.  Fixed points of multivalued nonexpansive maps , 1991 .

[192]  S. Naimpally,et al.  Extensions of some fixed point theorems of Rhoades , 1983 .

[193]  Li Nan On the Stability of Generalized f-Projection Operators with an Application , 2011 .

[194]  Poom Kumam,et al.  Algorithms of Common Solutions to Generalized Mixed Equilibrium Problems and a System of Quasivariational Inclusions for Two Difference Nonlinear Operators in Banach Spaces , 2011 .

[195]  Wataru Takahashi,et al.  Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem , 2007 .