Generalized viscosity approximation method for minimization and fixed point problems of quasi-pseudocontractive mappings in Hadamard spaces

Abstract

In this paper, we introduce a generalized viscosity method which includes a sequence of contractive mappings for approximating solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function together with a fixed point problem of countable infinite family of [Formula: see text]-Lipschitzian and quasi-pseudocontractive mappings in Hadamard spaces. We establish a strong convergence result without imposing a compactness condition of the proposed algorithm to an element in the intersection of the set of solutions of fixed point problem of finitely many resolvents of a lower semi-continuous function and fixed point problem of countable infinite family of quasi-pseudocontractive mappings. We display a numerical example to show the applicability of our main result. Our results complement and extend many recent results in literature.