Algorithm of a new variational inclusion problem and strictly pseudononspreading mapping with application

Abstract

The purpose of this research is to modify the variational inclusion problems and prove a strong convergence theorem for finding a common element of the set of fixed points of a κ-strictly pseudononspreading mapping and the set of solutions of a finite family of variational inclusion problems and the set of solutions of a finite family of equilibrium problems in Hilbert space. By using our main result, we prove a strong convergence theorem involving a κ-quasi-strictly pseudo-contractive mapping in Hilbert space. We give a numerical example to support some of our results.

An Inertial Forward–Backward Splitting Method for Solving Modified Variational Inclusion Problems and Its Application

“…Remark 3. Experimentally, the SNR value demonstrates that our proposed algorithm is more effective than the algorithm that was introduced by Khuangsatung and Kangtunyakarn [15,16] in solving the image recovery problem (41).…”

“…The numerical experiments and proof that the algorithm generated strong convergence results have been provided. Khuangsatung and Kangtunyakarn's modified variational inclusion problem (MVIP) [15,16]…”

“…This paper's purpose is to demonstrate an inertial forward-backward splitting method for solving the modified variational inclusion problem based on the concept of [11,15,16]. The proposed method modifies = method (18) for higher acceleration by using the inertial technique of Cholamjiak et al [11].…”

A Modified Tseng’s Method for Solving the Modified Variational Inclusion Problems and Its Applications

“…In 2014, Khuangsatung and Kangtunyakarn [27,28] presented the modified variational inclusion problem (MVIP), that is, to find u ∈ H such that the following holds:…”