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http://dx.doi.org/10.22771/nfaa.2022.27.01.02

GENERAL BICONVEX FUNCTIONS AND BIVARIATIONAL-LIKE INEQUALITIES  

Noor, Muhammad Aslam (Department of Mathematics, COMSATS University Islamabad)
Publication Information
Nonlinear Functional Analysis and Applications / v.27, no.1, 2022 , pp. 23-44 More about this Journal
Abstract
In this paper, we consider and introduce some new concepts of the biconvex functions involving an arbitrary bifunction and function. Some new relationships among various concepts of biconvex functions have been established. We have shown that the optimality conditions for the general biconvex functions can be characterized by a class of bivariational-like inequalities. Auxiliary principle technique is used to propose proximal point methods for solving general bivariational-like inequalities. We also discussed the conversance criteria for the suggested methods under pseudo-monotonicity. Our method of proof is very simple compared with methods. Several special cases are discussed as applications of our main concepts and results. It is a challenging problem to explore the applications of the general bivariational-like inequalities in pure and applied sciences.
Keywords
Biconvex functions; monotone operators; biconvex functions; strongly biconvex functions;
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Times Cited By KSCI : 3  (Citation Analysis)
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