On split equality problem for proximal point algorithm

Received: 12.III.2018, Accepted: 16.V.2018

Abstract. In this paper, we introduce a modified Mann iterative scheme for solving a split equality proximal point algorithm problem. We also establish strong convergence of this iterative sequence to a minimizer of a convex function which is also a common fixed point of a nonspreading-type multi-valued mapping in Hilbert space.

Keywords: Split equality, Proximal point algorithm, Fixed point, Nonexpansive mapping, Strong convergence

Mathematics Subject Classification (2010): 47H09, 47J25

Authors:
Oluwatosin Temitope Mewomo, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, SouthAfrica

Godwin Chidi Ugwunnadi, Department of Mathematics, University of Swaziland, Kwaluseni, Swaziland