On solving split best proximity point and equilibrium problems in Hilbert spaces

Abstract

In this paper, we introduce a split best proximity point and equilibrium problem, and find a solution of the best proximity point problem such that its image under a given bounded linear operator is a solution of the equilibrium problem. We construct an iterative algorithm to solve such problem in real Hilbert spaces and obtain a weak convergence theorem. Finally, we also give an example to illustrate our result.

An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings

“…4. For other related works that allow similar developments to the ones in the current paper, we refer the readers to Kingkam and Nantadilok [9], Padcharoen et al [13], Sharma and Chandok [15], Shi et al [16], Tiammee and Tiamme [17],...…”

Inertial Projection Algorithm for Solving Split Best Proximity Point and Mixed Equilibrium Problems in Hilbert Spaces

“…In Theorem 1, if we take g ≡ 0 and ϑ m = 0, we have the following result for solving the split best proximity problem and equilibrium problem which was initially studied and analyzed by Tiammee and Suantai [17].…”

“…In 2019, Tiammee and Suantai [17] proposed and studied the following iterative algorithm for solving the split best proximity point and equilibrium problems in Hilbert spaces:…”

“…Motivated and inspired by the work of Suantai et al [16] and Tiammee and Suantai [17] and ongoing work in this direction, we propose and analyze an iterative algorithm for solving the SBPMEP (10) and (11) and establish a weak convergence theorem. The results obtained in this paper can be considered as the common solution of the best proximity point problem and mixed equilibrium problem and is a generalization of the recently published work by Tiammee and Suantai [17]. The iterative algorithm and results discussed in this paper are novel and can be viewed as a generalization and refinement of previously published work in this field.…”