Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Existence results for nonexpansive multi-valued operators and nonlinear integral inclusions

Khaled Ben Amara, Aref Jeribi, Najib Kaddachi

Abstract

In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on nonempty, closed convex set of Banach algebras are also presented. These results improve and complement a number of earlier works. As an application, we prove existence results for a broad class of nonlinear functional integral inclusions as well as nonlinear differential inclusions.

Existence results for nonexpansive multi-valued operators and nonlinear integral inclusions

Abstract

In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on nonempty, closed convex set of Banach algebras are also presented. These results improve and complement a number of earlier works. As an application, we prove existence results for a broad class of nonlinear functional integral inclusions as well as nonlinear differential inclusions.
Paper Structure (5 sections, 18 theorems, 135 equations)

This paper contains 5 sections, 18 theorems, 135 equations.

Table of Contents

  1. Introduction
  2. Basics results
  3. Fixed point results for multi-valued mappings in Banach spaces
  4. Fixed Point results for multi-valued mappings in Banach algebras
  5. Nonlinear integral inclusions

Key Result

Theorem 2.1

amar2018 Let $K$ be a nonempty, closed and convex subset of a Banach space $E$ and let $F : K \longrightarrow \mathcal{P}_{cl,cv}(K)$ be a multi-valued operator such that: $(i)$$F$ maps weakly compact sets into weakly relatively compact sets, and $(ii)$$F$ is countably $\omega$-condensing with $w$-w

Theorems & Definitions (29)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Theorem 2.1
  • Theorem 3.1
  • Corollary 3.1
  • Corollary 3.2
  • Remark 3.1
  • ...and 19 more