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Volume 11
Issue 7
10.3390/axioms11070321
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Article

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

by
Shamshad Husain
1,
Faizan Ahmad Khan
2,*,
Mohd Furkan
3,
Mubashshir U. Khairoowala
1,* and
Nidal H. E. Eljaneid
2
1
Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
2
Computational and Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
3
University Polytechnic, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
*
Authors to whom correspondence should be addressed.
Axioms 2022, 11(7), 321; https://doi.org/10.3390/axioms11070321
Submission received: 21 May 2022 / Revised: 19 June 2022 / Accepted: 23 June 2022 / Published: 1 July 2022
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Abstract

The primary goal of this paper is to present and study an inertial projection algorithm for solving the split best proximity and mixed equilibrium problems. We find a solution of the best proximity problem in such a way that its image under a bounded linear operator is the solution of the mixed equilibrium problem under the setting of real Hilbert spaces. We construct an iterative algorithm for the proposed problem and prove a weak convergence theorem. Moreover, we deduce some consequences from the main convergence result. Finally, a numerical experiment is presented to demonstrate the convergence analysis of our algorithm. The methodology and results presented in this work improve and unify some previously published findings in this field.
Keywords: iterative algorithm; mixed equilibrium problem; best proximally nonexpansive mapping; weak convergence iterative algorithm; mixed equilibrium problem; best proximally nonexpansive mapping; weak convergence

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MDPI and ACS Style

Husain, S.; Khan, F.A.; Furkan, M.; Khairoowala, M.U.; Eljaneid, N.H.E. Inertial Projection Algorithm for Solving Split Best Proximity Point and Mixed Equilibrium Problems in Hilbert Spaces. Axioms 2022, 11, 321. https://doi.org/10.3390/axioms11070321

AMA Style

Husain S, Khan FA, Furkan M, Khairoowala MU, Eljaneid NHE. Inertial Projection Algorithm for Solving Split Best Proximity Point and Mixed Equilibrium Problems in Hilbert Spaces. Axioms. 2022; 11(7):321. https://doi.org/10.3390/axioms11070321

Chicago/Turabian Style

Husain, Shamshad, Faizan Ahmad Khan, Mohd Furkan, Mubashshir U. Khairoowala, and Nidal H. E. Eljaneid. 2022. "Inertial Projection Algorithm for Solving Split Best Proximity Point and Mixed Equilibrium Problems in Hilbert Spaces" Axioms 11, no. 7: 321. https://doi.org/10.3390/axioms11070321

APA Style

Husain, S., Khan, F. A., Furkan, M., Khairoowala, M. U., & Eljaneid, N. H. E. (2022). Inertial Projection Algorithm for Solving Split Best Proximity Point and Mixed Equilibrium Problems in Hilbert Spaces. Axioms, 11(7), 321. https://doi.org/10.3390/axioms11070321

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