Coincidence points, generalized I-nonexpansive multimaps, and applications

Abstract We establish coincidence point results for multimaps satisfying generalized I -nonexpansive type conditions. Several invariant approximation results are obtained as applications. A random coincidence point result is also proved and, as applications, random invariant approximation results are obtained. Our results unify, extend and complement several well-known results.

[1]  Naseer Shahzad,et al.  Invariant Approximations and R-Subweakly Commuting Maps , 2001 .

[2]  Invariant approximations, generalized -contractions, and -subweakly commuting maps , 2005 .

[3]  Coincidence points and $R$-weakly commuting maps , 2001 .

[4]  Tayyab Kamran,et al.  Coincidence and fixed points for hybrid strict contractions , 2004 .

[5]  N. Hussain,et al.  Deterministic and random coincidence point results for f -nonexpansive maps , 2006 .

[6]  M. Al-Thagafi Common Fixed Points and Best Approximation , 1996 .

[7]  K. Tan,et al.  Random Fixed-Point Theorems and Approximation in Cones , 1994 .

[8]  Pramila Srivastava,et al.  Fixed Point Theory and Best Approximation: The KKM-map Principle , 1997 .

[9]  Naseer Shahzad,et al.  COINCIDENCE POINTS AND R-SUBWEAKLY COMMUTING MULTIVALUED MAPS , 2003 .

[10]  E. Dozo,et al.  Multivalued nonexpansive mappings and opial's condition , 1973 .

[11]  Naseer Shahzad,et al.  Noncommuting selfmaps and invariant approximations , 2006 .

[12]  COINCIDENCE AND FIXED POINTS FOR COMPATIBLE AND RELATIVELY NONEXPANSIVE MAPS , 1993 .

[13]  D. O’Regan,et al.  Coincidence Points and Invariant Approximation Results for Multimaps , 2007 .

[14]  T. L Hicks,et al.  A note on fixed-point theorems , 1982 .

[15]  S. Sessa,et al.  A result in best approximation theory , 1988 .

[16]  G. Jungck,et al.  Commuting Mappings and Fixed Points , 1976 .

[17]  W. Dotson Fixed Point Theorems for Non‐Expansive Mappings on Star‐Shaped Subsets of Banach Spaces , 1972 .

[18]  L. Habiniak Fixed point theorems and invariant approximations , 1989 .

[19]  Salvatore Sessa,et al.  Fixed point theorems for compatible multi-valued and single-valued mappings , 1989 .

[20]  S. Sessa,et al.  FIXED POINT THEOREMS IN BEST APPROXIMATION THEORY , 1995 .

[21]  ON MULTIVALUED f-NONEXPANSIVE MAPS , 1999 .

[22]  Shigeru Itoh,et al.  Random fixed point theorems with an application to random differential equations in Banach spaces , 1979 .