Author(s)

José Atilio Guerrero¹, Odalis Mejía², Nelson Merentes²

¹Departamento de Matemática y Fsica, Universidad Nacional Experimental del Táchira, San Cristóbal, Venezuela.
²Departamento de Matemática, Universidad Central de Venezuela, Caracas, Venezuela.

We give a neccesary and sufficient condition on a function such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(·)-variation with variable exponent functions into itself is a Nemytskij com-position operator.

Generalized Variation, p(·)-Variation in Wiener’s Sense, Variable Exponent, Convergence, Helly’s Theorem, Local Operator

Guerrero, J. , Mejía, O. and Merentes, N. (2016) Locally Defined Operators and Locally Lipschitz Composition Operators in the Space WBVp(·)([a, b]). Advances in Pure Mathematics, 6, 727-744. doi: 10.4236/apm.2016.610059.