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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 555=27, 2023.

Original scientific paper

https://doi.org/10.21857/mwo1vc3ewy

New classes of higher order variational-like inequalities

Muhammad Aslam Noor ; Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
Khalida Inayat Noor ; Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Full text: english pdf 446 Kb

page 153-165

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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.

Keywords

Convex functions; preinvex functions; monotone operators; variational-like inequalities; iterative methods; convergence

Hrčak ID:

307493

URI

https://hrcak.srce.hr/307493

Publication date:

25.8.2023.

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