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IMCS/Publications/BASM/Issues/BASM n.1(95)-n2(96), 2021/

An iterative method for solving split minimization problem in Banach space with applications

Authors: L.O. Jolaoso, F.U. Ogbuisi and O.T. Mewomo

Abstract

The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in $p$-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.

Lateef Olakunle Jolaoso,
School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban, South Africa.
E-mail:

Ferdinard Udochukwu Ogbuisi
School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban, South Africa.

and
DSI-NRF Center of Excellence i Mathematical and
Statistical Sciences (CoE-MaSS), Johannesburg, South
Africa
E-mail:

Oluwatosin Temitope Mewomo
School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban, South Africa.
E-mail:



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