%0 Journal Article %T Uniform convexity in \(\ell_{p(\cdot)}\) %A Bachar, Mostafa %A Bounkhel, Messaoud %A Khamsi, Mohamed A. %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 10 %@ ISSN 2008-1901 %F Bachar2017 %X 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. %9 journal article %R 10.22436/jnsa.010.10.15 %U http://dx.doi.org/10.22436/jnsa.010.10.15 %P 5292--5299