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Volume 14
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Hybrid Projection Method for Common Solutions to Generalized Mixed Equilibrium Problems

by
Ghada AlNemer
1,
Rehan Ali
2,*,
Shazia Akhtar
2 and
Mohammad Farid
3
1
Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
2
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, Jammu and Kashmir, India
3
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 52571, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(17), 3224; https://doi.org/10.3390/math14173224
Submission received: 30 July 2026 / Revised: 27 August 2026 / Accepted: 3 September 2026 / Published: 6 September 2026
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Optimization Methods: Algorithms, Convergence Analysis, and Applications)
Versions Notes

Abstract

In this paper, we develop modified inertial hybrid projection methods to obtain common solutions of generalized mixed equilibrium problems involving monotone and Lipschitz continuous operators. The use of alternative half-space constructions reduces both projection steps and operator evaluations. Strong convergence is established under standard conditions. The proposed approach is further extended to common solutions of variational inequality problems, and numerical results are provided for illustration.
Keywords: mixed equilibrium; variational inequality; monotone and Lipschitz continuous mapping; iterative methods; hybrid extragradient method mixed equilibrium; variational inequality; monotone and Lipschitz continuous mapping; iterative methods; hybrid extragradient method

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MDPI and ACS Style

AlNemer, G.; Ali, R.; Akhtar, S.; Farid, M. Hybrid Projection Method for Common Solutions to Generalized Mixed Equilibrium Problems. Mathematics 2026, 14, 3224. https://doi.org/10.3390/math14173224

AMA Style

AlNemer G, Ali R, Akhtar S, Farid M. Hybrid Projection Method for Common Solutions to Generalized Mixed Equilibrium Problems. Mathematics. 2026; 14(17):3224. https://doi.org/10.3390/math14173224

Chicago/Turabian Style

AlNemer, Ghada, Rehan Ali, Shazia Akhtar, and Mohammad Farid. 2026. "Hybrid Projection Method for Common Solutions to Generalized Mixed Equilibrium Problems" Mathematics 14, no. 17: 3224. https://doi.org/10.3390/math14173224

APA Style

AlNemer, G., Ali, R., Akhtar, S., & Farid, M. (2026). Hybrid Projection Method for Common Solutions to Generalized Mixed Equilibrium Problems. Mathematics, 14(17), 3224. https://doi.org/10.3390/math14173224

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