Approximate common solution of variational inequality and fixed point problems for family of nonexpansive semigroup

摘要

In this paper, we prove a path convergence theorem and introduce a new iterative scheme for approximation of common element of fixed point sets of family of nonexpansive semigroup and the set of solutions of variational inequality problem for an α-inverse strongly accretive mapping in strictly convex q-uniformly smooth real Banach space. As an application, solution is given to the problem of finding a common element of fixed point sets of family of nonexpansive semigroup and the set of zeros of an α-inverse strongly accretive operator. The result obtained augment and generalize several existing results.