Strongly log-biconvex Functions and Applications

Abstract

In this paper, we consider some new classes of log-biconvex functions. Several properties of the log-biconvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-biconvex functions are obtained. New parallelogram laws are obtained as applications of the strongly log-biconvex functions. Optimality conditions of differentiable strongly log-biconvex are characterized by a class of bivariational inequalities. Results obtained in this paper can be viewed as significant improvement of previously known results.

Trifunction Bihemivariational Inequalities

“…We now recall some concepts of biconvex sets and biconvex functions, which are mainly due to Noor et al [21,22,23,24]. Definition 2.1.…”

“…We now suggest and analyze some new iterative methods for solving the trifunction bihemivariational inequality (2.1) using the auxiliary principle technique of Glowinski, Lions and Tremolieres [10] without the Bregman distance function as developed by Noor [16][17][18][19][20][21][22][23][24].…”

“…functions is called the biconvex functions. Noor et al [19,21,22,23,24,26,27] have studied some basic properties of the biconvex functions. It have been shown that the biconvex functions have characterizations as the convex functions enjoy.…”

“…It have been shown that the biconvex functions have characterizations as the convex functions enjoy. In particular, it have been shown that the optimization conditions of the differentiable biconvex functions are characterized by a class of variational inequalities, called the bivariational inequalities, see [19,21,22,23,24,26,27] and references therein.…”

Study of Log Convex Mappings in Fuzzy Aunnam Calculus via Fuzzy Inclusion Relation over Fuzzy-Number Space

“…Log-convex mappings, which include hypergeometric mappings such as Gamma and Beta, are crucial in a number of fields of pure and practical sciences. Strongly logbiconvex mappings were first discussed by Noor and Noor [15], who also looked at their characterization. It is demonstrated that the bivariational inequalities are a novel generalization of the variational inequalities that can be used to describe the optimality conditions of the biconvex mappings.…”