Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 153-165.

NEW CLASSES OF HIGHER ORDER VARIATIONAL-LIKE INEQUALITIES

Muhammad Aslam Noor and Khalida Inayat Noor

Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
e-mail: noormaslam@gmail.com
e-mail: khalidan@gmail.com

Abstract.   In this paper, we prove that the optimality conditions of the higher order convex functions are characterized by a class of variational inequalities, which is called the higher order variational inequality. Auxiliary principle technique is used to suggest an implicit method for solving higher order variational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

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

Key words and phrases.   Convex functions, preinvex functions, monotone operators, variational-like inequalities, iterative methods, convergence.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/mwo1vc3ewy

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