New Method for Computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems

Abdulmalik U. Bello; Markjoe O. Uba; Michael 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

Functional Analysis 2022-08-18 v3

Authors: Abdulmalik U. Bello , Markjoe O. Uba , Michael T. Omojola , Maria A. Onyido , Cyril I. Udeani

Abstract

Let $E = L_p, \; 1<p\leq 2,$ 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.

Keywords

monotone maps zeros approximation lebesgue spaces hammerstein integral equations fixed points convex optimization variational inequality

Cite

@article{arxiv.2112.11074,
  title  = {New Method for Computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems},
  author = {Abdulmalik U. Bello and Markjoe O. Uba and Michael T. Omojola and Maria A. Onyido and Cyril I. Udeani},
  journal= {arXiv preprint arXiv:2112.11074},
  year   = {2022}
}

New Method for Computing zeros of monotone maps in Lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems

Abstract

Keywords

Cite

Related papers