New method for computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems
1Institute of Mathematics, African University of Science and Technology, Abuja, Nigeria 2Department of Mathematics, University of Nigeria, Nsukka, Nigeria 3Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria 4Department of Mathematical Sciences, Northern Illinois University, USA 5Department of Mathematics and Statistics, Comenius University in Bratislava, Slovakia
Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 3, pp. 1-21
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Abdulmalik U. Bello; Markjoe O. Uba; Micheal T. Omojola; Maria A. Onyido; Cyril I. Udeani; Abdulmalik U. Bello; Markjoe O. Uba; Micheal T. Omojola; Maria A. Onyido; Cyril I. Udeani. New method for computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems. Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 3, pp. 1-21. http://geodesic.mathdoc.fr/item/AMUC_2022_91_3_a5/
@article{AMUC_2022_91_3_a5,
author = {Abdulmalik U. Bello and Markjoe O. Uba and Micheal T. Omojola and Maria A. Onyido and Cyril I. Udeani and Abdulmalik U. Bello and Markjoe O. Uba and Micheal T. Omojola and Maria A. Onyido and Cyril I. Udeani},
title = { New method for computing zeros of monotone maps in {Lebesgue} spaces with applications to integral equations, fixed points, optimization, and variational inequality problems},
journal = {Acta mathematica Universitatis Comenianae},
pages = {1--21},
year = {2022},
volume = {91},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2022_91_3_a5/}
}
TY - JOUR
AU - Abdulmalik U. Bello
AU - Markjoe O. Uba
AU - Micheal T. Omojola
AU - Maria A. Onyido
AU - Cyril I. Udeani
AU - Abdulmalik U. Bello
AU - Markjoe O. Uba
AU - Micheal T. Omojola
AU - Maria A. Onyido
AU - Cyril I. Udeani
TI - New method for computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems
JO - Acta mathematica Universitatis Comenianae
PY - 2022
SP - 1
EP - 21
VL - 91
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2022_91_3_a5/
ID - AMUC_2022_91_3_a5
ER -
%0 Journal Article
%A Abdulmalik U. Bello
%A Markjoe O. Uba
%A Micheal T. Omojola
%A Maria A. Onyido
%A Cyril I. Udeani
%A Abdulmalik U. Bello
%A Markjoe O. Uba
%A Micheal T. Omojola
%A Maria A. Onyido
%A Cyril I. Udeani
%T New method for computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems
%J Acta mathematica Universitatis Comenianae
%D 2022
%P 1-21
%V 91
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2022_91_3_a5/
%F AMUC_2022_91_3_a5
Let $E = L_p$, $1, and $A: E \to E^*$ be a bounded monotone map such that $0 \in R(A)$. In this paper, we introduce and study an algorithm for approximating zeros of $A$. Furthermore, we study the application of this algorithm to the approximation of Hammerstein integral equations, fixed points, convex optimization, and variational inequality problems. Finally, we present numerical and illustrative examples of our results and their applications.
