Strongly log-biconvex Functions and Applications

Noor, Muhammad Aslam; Noor, Khalida İnayat

doi:10.34198/ejms.7121.123

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…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.…”

Section: Preliminaries and Basic Resultsmentioning

confidence: 99%

“…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].…”

Section: Collapses To the Methods For Solving The Bivariational Inequalities (22)mentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Trifunction Bihemivariational Inequalities

Noor

2021

EJMS

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In this paper, we consider a new class of hemivariational inequalities, which is called the trifunction bihemivariational inequality. We suggest and analyze some iterative methods for solving the trifunction bihemivariational inequality using the auxiliary principle technique. The convergence analysis of these iterative methods is also considered under some mild conditions. Several special cases are also considered. Results proved in this paper can be viewed as a refinement and improvement of the known results.

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“…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.…”

Section: Preliminaries and Basic Resultsmentioning

confidence: 99%

Section: Collapses To the Methods For Solving The Bivariational Inequalities (22)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Trifunction Bihemivariational Inequalities

Noor

2021

EJMS

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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In this paper, with the use of newly defined class up and down log–convex fuzzy-number valued mappings, we offer a few new and original mappings defined by applying some mild restrictions over the definition of up and down log–convex fuzzy-number valued mapping. With the use of these mappings, we are able to develop partners of Fejér-type inequalities for up and down log–convexity, which improve upon certain previously established findings. The discussion also includes these mappings’ characteristics. Moreover, some nontrivial examples are also provided to prove the validation of our main results.

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Mixed Variational Inequalities and Nonconvex Analysis

Noor,

Noor

2024

EJMS

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In this expository paper, we provide an account of fundamental aspects of mixed variational inequalities with major emphasis on the computational properties, various generalizations, dynamical systems, nonexpansive mappings, sensitivity analysis and their applications. Mixed variational inequalities can be viewed as novel extensions and generalizations of variational principles. A wide class of unrelated problems, which arise in various branches of pure and applied sciences are being investigated in the unified framework of mixed variational inequalities. It is well known that variational inequalities are equivalent to the fixed point problems. This equivalent fixed point formulation has played not only a crucial part in studying the qualitative behavior of complicated problems, but also provide us numerical techniques for finding the approximate solution of these problems. Our main focus is to suggest some new iterative methods for solving mixed variational inequalities and related optimization problems using resolvent methods, resolvent equations, splitting methods, auxiliary principle technique, self-adaptive method and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis of the mixed variational inequalities is studied using the resolvent equations method. Iterative methods for solving some new classes of mixed variational inequalities are proposed and investigated. Our methods of discussing the results are simple ones as compared with other methods and techniques. Results proved in this paper can be viewed as significant and innovative refinement of the known results.

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Strongly log-biconvex Functions and Applications

Cited by 4 publications

References 20 publications

Trifunction Bihemivariational Inequalities

Trifunction Bihemivariational Inequalities

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

Mixed Variational Inequalities and Nonconvex Analysis

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