NEW ASPECTS OF PREINVEX EQUILIBRIUM EQUATION

Khalida Inayat Noor†, Muhammad Aslam Noor‡

Abstract: Some classes of general preinvex equilibrium equations are introduced and investigated. Using fixed point, auxiliary principle technique and dynamical systems coupled with finite difference approach, we suggest and analyze a number of several multistep iterative methods for solving the general preinvex equilibrium equations. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis of the preinvex equilibrium equations is also considered. Various special cases are discussed as applications of the main results. Several open problems are suggested for future research.

Keywords: equilibrium equations, convex functions, fixed point iterative methods, auxiliary principle technique, dynamical system, convergence, sensitivity analysis.

MSC: 26D15, 26D10, 49J40, 65N35, 49J40, 90C26, 90C30.

DOI 10.56082/annalsarscimath.2026.4.87

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*Accepted for publication on July 12, 2026
†inayat.noor@uow.edu.pk, Department of Mathematics, University of Wah, Wah Cantt, Pakistan
‡aslam.noor@uow.edu.pk, Department of Mathematics, University of Wah, Wah Cantt, Pakistan

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997