Hybrid fixed point theory for strictly monotone increasing multi-valued mappings with applications

In this paper, a general hybrid fixed point theorem for the strict monotone increasing multi-valued mappings in ordered Banach spaces is proved via measure of noncompactness and it is further applied to perturbed functional nonconvex differential inclusions for proving the existence results for the extremal solutions under mixed Lipschitz, compactness and strict monotonic conditions.

[1]  A. Rodkina,et al.  Measures of noncompactness and condensing operators , 1992 .

[2]  J. Hale.  Theory of Functional Differential Equations , 1977 .

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

[4]  Multivalued differential inequalities , 1990 .

[5]  Bapurao C. Dhage.  HYBRID FIXED POINT THEORY AND EXISTENCE OF EXTREMAL SOLUTIONS FOR PERTURBED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS , 2007 .

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

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

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

[9]  Bapurao C. Dhage,et al.  Fixed-point theorems for discontinuous multivalued operators on ordered spaces with applications , 2006, Comput. Math. Appl..

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

[11]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

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

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

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

[15]  Ravi P. Agarwal,et al.  Stability of Partial Functional Integro-Differential Equations , 2006 .

[16]  B. Dhage,et al.  A functional differential equation in Banach algebras , 2005 .