Open AccessNew Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem
Author(s) -
Austine Efut Ofem,
Unwana Effiong Udofia,
Donatus Ikechi Igbokwe
Publication year - 2021
Publication title -
european journal of mathematical analysis
Language(s) - English
Resource type - Journals
ISSN - 2733-3957
DOI - 10.28924/ada/ma.1.106
Subject(s) - iterative method , algorithm , contraction (grammar) , mathematics , regular polygon , fixed point , minification , convergence (economics) , mathematical optimization , rate of convergence , contraction mapping , computer science , mathematical analysis , geometry , channel (broadcasting) , computer network , medicine , economics , economic growth
The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Also, we show that our proposed iterative algorithm converges weakly and strongly to the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Furthermore, it is proved analytically that our new iterative algorithm converges faster than one of the leading iterative algorithms in the literature for almost contraction mappings. Some numerical examples are also provided and used to show that our new iterative algorithm has better rate of convergence than all of S, Picard-S, Thakur and M iterative algorithms for almost contraction mappings and generalized α-nonexpansive mappings. Again, we show that the proposed iterative algorithm is stable with respect to T and data dependent for almost contraction mappings. Some applications of our main results and new iterative algorithm are considered. The results in this article are improvements, generalizations and extensions of several relevant results existing in the literature.