New Iterative Algorithm for Two Infinite Families of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces

We introduce a new iterative scheme for finding a common fixed point of two countable families of multivalued quasi-nonexpansive mappings and prove a weak convergence theorem under the suitable control conditions in a uniformly convex Banach space. We also give a new proof method to the iteration in the paper of Abbas et al. (2011).

[1]  Poom Kumam,et al.  Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces , 2010, Comput. Math. Appl..

[2]  Poom Kumam,et al.  A general iterative algorithm for the solution of variational inequalities for a nonexpansive semigroup in Banach spaces , 2011 .

[3]  Shihuang Hong,et al.  Fixed points of multivalued operators in ordered metric spaces with applications , 2010 .

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

[5]  Poom Kumam,et al.  Viscosity approximation methods based on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces , 2013, Math. Comput. Model..

[6]  J. Schu,et al.  Weak and strong convergence to fixed points of asymptotically nonexpansive mappings , 1991, Bulletin of the Australian Mathematical Society.

[7]  K. P. R. Sastry,et al.  Convergence of Ishikawa Iterates for a Multi-Valued Mapping with a Fixed Point , 2005 .

[8]  Poom Kumam,et al.  A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces , 2011, Int. J. Math. Math. Sci..

[9]  J. T. Markin.  Continuous dependence of fixed point sets , 1973 .

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

[11]  Ravi P. Agarwal,et al.  Applications of Fixed Point Theorems , 2009 .

[12]  Ravi P. Agarwal,et al.  Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme , 2011, Appl. Math. Lett..

[13]  C. E. Chidume,et al.  Geometric Properties of Banach Spaces and Nonlinear Iterations , 2009 .

[14]  Suthep Suantai,et al.  A Hybrid Method for a Countable Family of Multivalued Maps, Equilibrium Problems, and Variational Inequality Problems , 2010 .

[15]  Poom Kumam,et al.  Iterative methods for variational inequality problems and fixed point problems of a countable family of strict pseudo-contractions in a q-uniformly smooth Banach space , 2012 .

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

[17]  Convergence Theorems for Infinite Family of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces , 2012 .

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

[19]  Poom Kumam,et al.  An iterative procedure for solving the common solution of two total quasi-ϕ-asymptotically nonexpansive multi-valued mappings in Banach spaces , 2013 .

[20]  Jong-Yeoul Park,et al.  Strong convergence theorems for nonexpansive mappings in banach spaces , 1996 .

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

[22]  Mujahid Abbas,et al.  Fixed point theorems for two new classes of multivalued mappings , 2009, Appl. Math. Lett..

[23]  Isa Yildirim,et al.  A one-step iterative process for two multivalued nonexpansive mappings in Banach spaces , 2011, Comput. Math. Appl..

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