Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Symmetry

MohamedA Khamsi¹  ButhinahA. Bin Dehaish² 

[1] Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA;Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, Jeddah 21593, Saudi Arabia;

关键词: asymptotically nonexpansive mapping;    Fibonacci sequence;    fixed point;    Mann iteration process;    modular function spaces;    monotone Lipschitzian mapping;    opial condition;    uniformly convexity;   

DOI  :  10.3390/sym10100481

来源: DOAJ

【 摘 要 】

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined byxn + 1 =t n Tϕ ( n )(x n)+( 1 −t n) x n, for n ∈ N, when T is a monotone asymptotically nonexpansive self-mapping.

【 授权许可】

Unknown