Generalized Hybrid Viscosity-Type Forward-Backward Splitting Method with Application to Convex Minimization and Image Restoration Problems

Abstract

Let E be a uniformly convex and q-uniformly smooth real Banach space. Let be an α- inverse strongly accretive mapping of order q, be a set-valued m- accretive mapping and be a nonexpansive mapping. In this article, a viscosity-type forward-backward splitting method for approximating a zero of (A + B) which is also a fixed point of S is introduced studied. Strong convergence theorem of the method is proved under suitable conditions. Furthermore, the convergence result obtained is applied to convex minimization and image restoration problems. Finally, numerical illustrations are presented to compare the convergence of the sequence of our algorithm and that of some recent important algorithms.