Fixed points of multivalued operators in ordered metric spaces with applications

Abstract The purpose of this paper is to present some new (hybrid) fixed point theorems involving multivalued operators which satisfy weakly generalized contractive conditions in an ordered complete metric space. An example of the existence of solutions for a perturbed impulsive hyperbolic differential inclusion with variable times is given to illustrate the usability of our results.

[1]  B. Rhoades,et al.  A comparison of various definitions of contractive mappings , 1977 .

[2]  Shihuang Hong,et al.  Fixed points of discontinuous multivalued increasing operators in Banach spaces with applications , 2003 .

[3]  Minjian Shen,et al.  Common fixed points for generalized contractive multivalued operators in complete metric spaces , 2009, Appl. Math. Lett..

[4]  Salvatore Sessa,et al.  ON A WEAK COMMUTATIVITY CONDITION OF MAPPINGS IN FIXED POINT CONSIDERATIONS , 1982 .

[5]  Juan J. Nieto,et al.  Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations , 2005, Order.

[6]  A. Aliouche Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions , 2008 .

[7]  Dongxue Guan,et al.  Hybrid fixed points of multivalued operators in metric spaces with applications , 2009 .

[8]  Robert Plebaniak,et al.  Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions , 2009 .

[9]  B. E. Rhoades,et al.  A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type , 2005, Int. J. Math. Math. Sci..

[10]  M. Benchohra,et al.  Existence results for impulsive hyperbolic differential inclusions , 2003 .

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

[12]  A. Branciari,et al.  A FIXED POINT THEOREM FOR MAPPINGS SATISFYING A GENERAL CONTRACTIVE CONDITION OF INTEGRAL TYPE , 2002 .

[13]  V. Lakshmikantham,et al.  Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces , 2009 .

[14]  Dariusz Wardowski,et al.  Fixed point theorems for set-valued contractions in complete metric spaces , 2007 .

[15]  A. PetruÅŸel Multivalued operators and fixed points , 2000 .

[16]  Existence theory for perturbed impulsive hyperbolic differential inclusions with variable times , 2007 .

[17]  A. A. Tolstonogov,et al.  Di erential Inclusions in a Banach Space , 2010 .

[18]  B. Dhage,et al.  Multi-valued mappings and fixed points II , 2006 .

[19]  J. Harjani,et al.  Fixed point theorems for weakly contractive mappings in partially ordered sets , 2009 .

[20]  Bapurao C. Dhage,et al.  On a fixed point theorem in Banach algebras with applications , 2005, Appl. Math. Lett..

[21]  Dariusz Wardowski,et al.  Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces , 2009 .

[22]  M. Benchohra,et al.  Impulsive hyperbolic differential inclusions with variable times , 2003 .

[23]  R. Kannan,et al.  Some results on fixed points , 1968 .

[24]  Donal O'Regan,et al.  Fixed point theorems for generalized contractions in ordered metric spaces , 2008 .

[25]  A. Aliouche,et al.  Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type , 2007 .

[26]  Juan J. Nieto,et al.  Applications of Contractive-like Mapping Principles to Fuzzy Equations , 2006 .

[27]  B. Dhage,et al.  A general multi-valued hybrid fixed point theorem and perturbed differential inclusions , 2006 .

[28]  B. Rhoades,et al.  Some theorems on weakly contractive maps , 2001 .

[29]  Ravi P. Agarwal,et al.  Generalized contractions in partially ordered metric spaces , 2008 .

[30]  Shihuang Hong,et al.  Fixed points for mixed monotone multivalued operators in Banach spaces with applications , 2008 .

[31]  B. Dhage,et al.  MULTI-VALUED OPERATORS AND FIXED POINT THEOREMS IN BANACH ALGEBRAS I , 2006 .

[32]  G. Marino Nonlinear boundary value problems for multivalued differential equations in Banach spaces , 1990 .

[33]  Yeol Je Cho,et al.  COMPATIBLE MAPPINGS OF TYPE (A) AND COMMON FIXED POINTS , 1993 .

[34]  B. Rhoades,et al.  Two fixed-point theorems for mappings satisfying a general contractive condition of integral type , 2003 .

[35]  Bapurao C. Dhage,et al.  Hybrid fixed point theory for strictly monotone increasing multi-valued mappings with applications , 2007, Comput. Math. Appl..