Approximating Fixed Points of The General Asymptotic Set Valued Mappings

Salwa Salman Abed

doi:10.24297/jam.v18i.8549

Authors

Salwa Salman Abed College of Education

DOI:

https://doi.org/10.24297/jam.v18i.8549

Keywords:

Asymptotically Non- Expansive Set-Valued Mappings, Demi-Closeness, Fixed Points, Iterative Schemes

Abstract

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 y_n+1 = t_n z+ (1-t_n )u_n , u_n in Gⁿ( y_n ) 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

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Author Biography

Salwa Salman Abed, College of Education

Department of Mathematics, for Pure Sciences ibn Al-Haitham,

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