MULTI-VALUED OPERATORS AND FIXED POINT THEOREMS IN BANACH ALGEBRAS I

In this paper the multi-valued versions of some well-known hybrid fixed point theorems of Dhage [6, 7] in Banach algebras are proved. As an application, an existence theorem for a certain integral inclusion in Banach algebras is proved.

[1]  Shouchuan Hu,et al.  Handbook of multivalued analysis , 1997 .

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

[3]  L. Górniewicz Topological Fixed Point Theory of Multivalued Mappings , 1999 .

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

[5]  E. Zeidler Nonlinear functional analysis and its applications , 1988 .

[6]  D. O'Regan,et al.  A Fixed Point Theorem in Banach Algebras with Applications to Functional Integral Equations , 2004 .

[7]  Multivalued Operators and Fixed-Point Theorems in Banach Algebras II , 2005 .

[8]  D. O’Regan New fixed-points results for 1-set contractive set valued maps , 1998 .

[9]  W. Petryshyn,et al.  A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings , 1974 .

[10]  M. A. Krasnoselʹskii Topological methods in the theory of nonlinear integral equations , 1968 .

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

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

[13]  L. Rybiński An application of the continuous selection theorem to the study of the fixed points of multivalued mappings , 1990 .

[14]  K. Deimling Multivalued Differential Equations , 1992 .

[15]  M. Kisielewicz Differential Inclusions and Optimal Control , 1991 .

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

[17]  F. Browder Nonlinear Functional Analysis and Its Applications, Part 1 , 1986 .