Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions

summary:In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage (Dhage, B. C., A fixed point theorem for multivalued mappings on ordered Banach spaces with applications I, Nonlinear Anal. Forum 10 (2005), 105–126.) under weaker convexity conditions

Some Coupled coincidence and common fixed point theorems for hybrid pair of mappings

In this paper we extend the multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Keywords: coupled common fixed point, coupled coincidence point, coupled point of coincidence, w-compatible mappings, F-weakly commuting mappings

Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi--Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors

Strong Convergence Theorems under Hybrid Methods for Two Nonlinear Mappings in Banach Spaces (Study on Nonlinear Analysis and Convex Analysis)

In this article, using the hybrid method defined by Nakajo and Takahashi [17], we first obtain a strong convergence theorem for two noncommutative nonlinear mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota [25], we prove another strong convergence theorem for the mappings in a Banach space. Using these results, we get well-known and new strong convergence theorems by the hybrid method and the shrinking projection method in a Hilbert space and a Banach space