Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 261-281.

AUXILIARY PRINCIPLE TECHNIQUE FOR SOLVING TRIFUNCTION HARMONIC VARIATIONAL INEQUALITIES

Muhammad Aslam Noor and Khalida Inayat Noor

Abstract.   In this paper, we introduce and investigate some new classes of trifunction harmonic variational inequalities. Several important new problems are obtained as special cases. Some new harmonic Bregman distance functions are derived for the Shannon entropy and Burg entropy harmonic convex functions. The auxiliary principle technique involving the harmonic Bregman distance function is applied to suggest and analyze some hybrid inertial iterative methods for solving the trifunction harmonic variational inequality. The convergence analysis of these iterative methods is also considered under some mild conditions. Some special cases are also pointed out. Results proved in this paper can be viewed as a refinement and improvement of the known results.

2020 Mathematics Subject Classification.   49J40, 90C33, 26D15, 26A51.

Key words and phrases.   Harmonic variational inequalities, harmonic convex functions, auxiliary principle, proximal methods, convergence.

DOI: https://doi.org/10.21857/yrvgqt31w9

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