On a New Approximation for Weighted Integral-Type Inequalities in V ELS

Abstract

The variable exponent Lebesgue spaces are of interest for their applications to modeling problems in physics and to the study of variational integrals and partial differential equations with non-standard growth conditions. We refer to [1-7]. This studies also has been stimulated by problems of elasticity, fluid dynamics, calculus of variations and differential equations with non-standard growth conditions. More results for Hardy-type inequalities in variable exponent Lebesgue spaces can be found in F. I. Mamedov et al., [9]; L. Akın [10, 11]; A. Kufner and L. E. Persson [14]; V. Kokilashvili and S. Samko [15] and references therein