Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence

Samet Maldar; Esra Çetin

doi:10.36753/mathenot.1799797

Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence

Abstract

In this paper, we give comprehensive details about iteration methods to solve equilibrium problems through viscosity type approximation. This study introduces a new viscosity type iteration method in order to find the common point of the set of fixed points of nonexpansive mappings and relaxed $(a,b)$-cocoercive mapping, and the groups of solutions for of variational inequality and an equilibrium problem in Hilbert spaces. We also argue that this iteration method strongly converges to a common point in the mentioned three sets. As part of the applications, we give an example supporting the convergence theorem. As we emphasize the concept of data dependency for fixed point theory, we present the data dependence result for the fixed points of the stated class of mappings for the novel iteration method via viscosity type approximation.

Keywords

Equilibrium problem, data dependence, iteration method, viscosity approximation methods

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Samet Maldar ^*
0000-0002-2083-899X
Türkiye

Esra Çetin
0009-0005-7630-2640
Türkiye

Early Pub Date

February 9, 2026

Publication Date

February 9, 2026

Submission Date

October 8, 2025

Acceptance Date

December 31, 2025

Published in Issue

Year 2026 Volume: 14 Number: 1

DOI

https://doi.org/10.36753/mathenot.1799797

IZ

https://izlik.org/JA54UJ94LB

APA

Maldar, S., & Çetin, E. (2026). Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence. Mathematical Sciences and Applications E-Notes, 14(1), 1-20. https://doi.org/10.36753/mathenot.1799797

AMA

1.Maldar S, Çetin E. Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence. Math. Sci. Appl. E-Notes. 2026;14(1):1-20. doi:10.36753/mathenot.1799797

Chicago

Maldar, Samet, and Esra Çetin. 2026. “Solutions of Equilibrium Problems With Fixed Point Iteration Method and Data Dependence”. Mathematical Sciences and Applications E-Notes 14 (1): 1-20. https://doi.org/10.36753/mathenot.1799797.

EndNote

Maldar S, Çetin E (March 1, 2026) Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence. Mathematical Sciences and Applications E-Notes 14 1 1–20.

IEEE

[1]S. Maldar and E. Çetin, “Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence”, Math. Sci. Appl. E-Notes, vol. 14, no. 1, pp. 1–20, Mar. 2026, doi: 10.36753/mathenot.1799797.

ISNAD

Maldar, Samet - Çetin, Esra. “Solutions of Equilibrium Problems With Fixed Point Iteration Method and Data Dependence”. Mathematical Sciences and Applications E-Notes 14/1 (March 1, 2026): 1-20. https://doi.org/10.36753/mathenot.1799797.

JAMA

1.Maldar S, Çetin E. Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence. Math. Sci. Appl. E-Notes. 2026;14:1–20.

MLA

Maldar, Samet, and Esra Çetin. “Solutions of Equilibrium Problems With Fixed Point Iteration Method and Data Dependence”. Mathematical Sciences and Applications E-Notes, vol. 14, no. 1, Mar. 2026, pp. 1-20, doi:10.36753/mathenot.1799797.

Vancouver

1.Samet Maldar, Esra Çetin. Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence. Math. Sci. Appl. E-Notes. 2026 Mar. 1;14(1):1-20. doi:10.36753/mathenot.1799797