H(·, ·)-Co-Accretive Mapping with an Application for Solving a System of Variational Inclusions

Rais Ahmad, B.S. Lee, Mohd. Akram

Abstract

In this paper, we define a new class of H(,)-co-accretive mappings which are the sum of symmetric cocoercive mappings and symmetric accretive mappings. We prove that the resolvent operator associated with H(,)-coaccretive mapping is single-valued and Lipschitz continuous. Furthermore, we apply these new results to solve a system of variational inclusions in real q-uniformly smooth Banach spaces. Our results are extensions and improvements of some known results existing in the literature. An illustrative example is also given.