Open AccessApproximating Fixed Points of The General Asymptotic Set Valued Mappings
Author(s) -
Salwa Salman Abed
Publication year - 2020
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v18i.8549
Subject(s) - mathematics , fixed point , banach space , sequence (biology) , generalization , fixed point theorem , convergence (economics) , closeness , discrete mathematics , expansive , set (abstract data type) , pure mathematics , mathematical analysis , genetics , compressive strength , materials science , economics , composite material , biology , economic growth , computer science , programming language
The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by yn+1 = tn z+ (1-tn )un , un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved