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


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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