Convergence theorem for an intermixed iteration in $p$-uniformly convex metric space

Abstract

In this paper, we first introduce the intermixed algorithm in $p$-uniformly convex metric spaces, and then we prove $\Delta$-convergence of the proposed iterative method for finding a common element of the sets of fixed points of finite families of nonexpansive mappings in the framework of complete $p$-uniformly convex metric spaces. Furthermore, we apply our main theorem to prove $\Delta$-convergence to solve the minimization problems in the framework of complete $p$-uniformly convex metric spaces. Finally, we give two examples in $L^p$ spaces and numerical examples to support our main results.