General Preinvex Functions and Variational-Like Inequalities

Muhammad Aslam Noor, Khalida Inayat Noor, Bandar Mohsen (), Michael Th. Rassias () and Andrei Raigorodskii ()
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Muhammad Aslam Noor: COMSATS University Islamabad
Khalida Inayat Noor: COMSATS University Islamabad
Bandar Mohsen: King Saud University
Michael Th. Rassias: University of Zurich
Andrei Raigorodskii: Moscow Institute of Physics and Technology

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 643-666 from Springer

Abstract: Abstract In this paper, we define and introduce some new concepts of the higher order strongly general preinvex functions and higher order strongly monotone operators involving the arbitrary bifunction. Some new relationships among various concepts of higher order strongly general preinvex functions have been established. It is shown that the new parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine general preinvex functions, which is itself a novel application. It is proved that the optimality conditions of the higher order strongly general preinvex functions are characterized by a class of variational inequalities, which are called the higher order strongly general variational-like inequalities. An auxiliary principle technique is used to suggest an implicit method for solving strongly general variational-like inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases are also discussed. Results obtained in this paper can be viewed as a refinement and improvement of previously known results.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_35

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DOI: 10.1007/978-3-030-84122-5_35

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