Variational-like inclusion involving infinite family of set-valued mappings governed by resolvent equations
Abstract
The purpose of this work is to investigate generalized H(.,.,.)-ϕ-η-cocoercive operator and use its application via resolvent equation approach to solve the variational-like inclusion involving infinite family of set-valued mappings in semi-inner product spaces. We aim to establish an equivalence between the set-valued variational-like inclusion problem and fixed point problem. A relationship also obtain between the set-valued variational-like inclusion problem and the resolvent equation problem. This equivalent formulation suggests an idea to construct an iterative algorithm to find a solution of the resolvent equation problem.
Copyright © 2021 Sanjeev Gupta, Manoj Singh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. Gupta, M. Singh, Variational-like inclusion involving infinite family of set-valued mappings governed by resolvent equations, J. Math. Comput. Sci. 11 (2021), 874–892. https://doi.org/10.28919/jmcs/5177
BibTeX
@article{Gupta2021,
author = {Gupta, Sanjeev and Singh, Manoj},
title = {Variational-like inclusion involving infinite family of set-valued mappings governed by resolvent equations},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {874--892},
doi = {10.28919/jmcs/5177}
}