TY - JOUR AU - Bachar, Mostafa AU - Bounkhel, Messaoud AU - Khamsi, Mohamed A. PY - 2017 TI - Uniform convexity in \(\ell_{p(\cdot)}\) JO - Journal of Nonlinear Sciences and Applications SP - 5292--5299 VL - 10 IS - 10 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.10.15 DO - 10.22436/jnsa.010.10.15 ID - Bachar2017 ER - TY - BOOK TI - Introduction to Banach Spaces and Their Geometry AU - B. Beauzamy PB - North-Holland PY - 1985 DA - 1985// CY - Amsterdam ID - Beauzamy 1985 ER - TY - JOUR TI - Uniformly Convex Spaces AU - J. A. Clarkson JO - Trans. Amer. Math. Soc. PY - 1936 DA - 1936// VL - 40 ID - Clarkson 1936 ER - TY - BOOK TI - Lebesgue and Sobolev Spaces with Variable Exponents AU - L. Diening AU - P. Harjulehto AU - P. Hästö AU - M. Růžička PB - Springer PY - 2011 DA - 2011// CY - Berlin ID - Diening2011 ER - TY - BOOK TI - An Introduction to Metric Spaces and Fixed Point Theory AU - M. A. Khamsi AU - W. A. Kirk PB - Wiley-Interscience PY - 2011 DA - 2011// CY - New York ID - Khamsi2011 ER - TY - BOOK TI - Fixed Point Theory in Modular Function Spaces AU - M. A. Khamsi AU - W. M. Kozlowski PB - Birkhauser PY - 2015 DA - 2015// CY - New York ID - Khamsi2015 ER - TY - JOUR TI - Fixed point theory in modular function spaces AU - M. A. Khamsi AU - W. K. Kozlowski AU - S. Reich JO - Nonlinear Anal. PY - 1990 DA - 1990// VL - 14 ID - Khamsi1990 ER - TY - JOUR TI - A fixed point theorem for mappings which do not increase distances AU - W. A. Kirk JO - Amer. Math. Monthly PY - 1965 DA - 1965// VL - 72 ID - Kirk1965 ER - TY - JOUR TI - Summability in \(\ell(p_{11}, p_{21}, ...)\) Spaces AU - V. Klee JO - Studia Math. PY - 1965 DA - 1965// VL - 25 ID - Klee1965 ER - TY - JOUR TI - On spaces \(L^{p(x)}\) and \(W^{1,p(x)}\) AU - O. Kováčik AU - J. Rákosník JO - Czechoslovak Math. J. PY - 1991 DA - 1991// VL - 41 ID - Kováčik1991 ER - TY - BOOK TI - Modular Function Spaces AU - W. M. Kozlowski PB - Marcel Dekker PY - 1988 DA - 1988// CY - New York ID - Kozlowski1988 ER - TY - BOOK TI - Orlicz spaces and modular spaces AU - J. Musielak PB - Springer-Verlag PY - 1983 DA - 1983// CY - Berlin ID - Musielak 1983 ER - TY - BOOK TI - Modulared Semi-ordered Linear Spaces AU - H. Nakano PB - Maruzen Co. PY - 1950 DA - 1950// CY - Tokyo ID - Nakano1950 ER - TY - JOUR TI - Modulared sequence spaces AU - H. Nakano JO - Proc. Japan Acad. PY - 1951 DA - 1951// VL - 27 ID - Nakano 1951 ER - TY - BOOK TI - Topology of linear topological spaces AU - H. Nakano PB - Maruzen Co. Ltd. PY - 1951 DA - 1951// CY - Tokyo ID - Nakano 1951 ER - TY - JOUR TI - Über konjugierte Exponentenfolgen AU - W. Orlicz JO - Studia Math. PY - 1931 DA - 1931// VL - 3 ID - Orlicz1931 ER - TY - JOUR TI - On the modeling of electrorheological materials AU - K. Rajagopal AU - M. Růžička JO - Mech. Research Comm. PY - 1996 DA - 1996// VL - 23 ID - Rajagopal1996 ER - TY - BOOK TI - Electrorheological fluids: modeling and mathematical theory AU - M. Růžička PB - Springer-Verlag PY - 2000 DA - 2000// CY - Berlin ID - Růžička2000 ER - TY - JOUR TI - Uniform convexity of Banach spaces \(\ell(\{p_i\})\) AU - K. Sundaresan JO - Studia Math. PY - 1971 DA - 1971// VL - 39 ID - Sundaresan1971 ER - TY - JOUR TI - Reflexivity and Summability: The Nakano \(\ell(p_i)\) spaces AU - D. Waterman AU - T. Ito AU - F. Barber AU - J. Ratti JO - Studia Math. PY - 1969 DA - 1969// VL - 33 ID - Waterman1969 ER -