Uniform convexity in \(\ell_{p(\cdot)}\)

The Journal of Nonlinear Sciences and its Applications

Mohamed A.Khamsi¹  MostafaBachar²  MessaoudBounkhel² 

[1] Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA;Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia

关键词: Fixed point;    modular vector spaces;    nonexpansive mapping;    uniformly convex;    variable exponent spaces;   

DOI  :  10.22436/jnsa.010.10.15

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

In this work, we investigate the variable exponent sequence space \(\ell_{p(\cdot)}\).In particular, we prove a geometric property similar to uniform convexity without the assumption \(\limsup_{n \to \infty} p(n) < \infty\).This property allows us to prove the analogue to Kirk's fixed point theorem in the modular vector space \(\ell_{p(\cdot)}\) under Nakano's formulation.

【 授权许可】

Unknown