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

Volume 10, Issue 10, pp 5292--5299 http://dx.doi.org/10.22436/jnsa.010.10.15

Publication Date: October 20, 2017 Submission Date: May 09, 2017

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Authors

Mostafa Bachar - Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia. Messaoud Bounkhel - Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia. Mohamed A. Khamsi - Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. - Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA.

Abstract

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.

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ISRP Style

Mostafa Bachar, Messaoud Bounkhel, Mohamed A. Khamsi, Uniform convexity in \(\ell_{p(\cdot)}\), Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5292--5299

AMA Style

Bachar Mostafa, Bounkhel Messaoud, Khamsi Mohamed A., Uniform convexity in \(\ell_{p(\cdot)}\). J. Nonlinear Sci. Appl. (2017); 10(10):5292--5299

Chicago/Turabian Style

Bachar, Mostafa, Bounkhel, Messaoud, Khamsi, Mohamed A.. "Uniform convexity in \(\ell_{p(\cdot)}\)." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5292--5299

Keywords

Fixed point
modular vector spaces
nonexpansive mapping
uniformly convex
variable exponent spaces

MSC

47H09
46B20
47H10
47E10

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