Generalized mixed equilibrium problems and quasi- ϕ-asymptotically nonexpansive multivalued mappings in Banach spaces

In this paper, we introduce two iterative algorithms for finding a common element of the set of fixed points of a quasi- ϕ-asymptotically nonexpansive multivalued mapping and the sets of solutions of generalized mixed equilibrium problem in Banach space. Then, we prove strong and weak convergence of the sequences to element in the mentioned set. Our results generalize and improve recent results announced by many authors.

Convergence Theorems for a Common Point of Solutions of Equilibrium and Fixed Point of Relatively Nonexpansive Multivalued Mapping Problems

We introduce an iterative process which converges strongly to a common point of set of solutions of equilibrium problem and set of fixed points of finite family of relatively nonexpansive multi-valued mappings in Banach spaces.

Strong Convergence Theorems for Modifying Halpern Iterations for Quasi--Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications

An iterative sequence for quasi--asymptotically nonexpansive multivalued mapping for modifying Halpern's iterations is introduced. Under suitable conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in the work by Chang et al. 2011.

Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications

The purpose of this paper is to present the notion of weak relatively nonexpansive multi-valued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces. The weak relatively nonexpansive multivalued mappings are more generalized than relatively nonexpansive multivalued mappings. In this paper, an example will be given which is a weak relatively nonexpansive multivalued mapping but not a relatively nonexpansive multivalued mapping. In order to get the strong convergence theorems for weak relatively nonexpansive multivalued mappings, a new monotone hybrid iteration algorithm with generalized (metric) projection is presented and is used to approximate the fixed point of weak relatively nonexpansive multivalued mappings. In this paper, the notion of multivalued resolvent of maximal monotone operator has been also presented which is a weak relatively nonexpansive multivalued mapping and can be used to find the zero point of maximal monotone operator.

Approximation of *-nonexpansive random multivalued operators on Banach spaces

We establish the existence and approximation of solutions to the operator inclusion y ∈ Ty for deterministic and random cases for a nonexpansive and *-nonexpansive multivalued mapping T defined on a closed bounded (not necessarily convex) subset C of a Banach space. We also prover random fixed points and approximation results for*-nonexpansive random operators defined on an unbounded subject C of a uniformly convex Banach space.