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Generalized Rectangular Convexity
In this paper we investigate the tr-convexity and the rectangular biconvexity in Euclidean spaces.
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Convexity—Tangents
We obtain some useful results using the fact that the graph of a convex function lies above its tangent lines. We lean heavily on convexity to show...
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Convex Isoquants in DEA Models with Selective Convexity
AbstractModels with selective convexity are an important class of data envelopment analysis (DEA) models. This type of model allows managers to...
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Games and the Treatment Convexity of Cancer
Evolutionary game theory has been highly valuable in studying frequency-dependent selection and growth between competing cancer phenotypes. We study...
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On the Jensen convexity of quasideviation and Bajraktarević means
Motivated by the characterization theorem about the Jensen convexity of quasiarithmetic means obtained by the authors in 2021, our main goal is to...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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Convexity of Non-homogeneous Quadratic Functions on the Hyperbolic Space
In this paper, some concepts related to the intrinsic convexity of non-homogeneous quadratic functions on the hyperbolic space are studied. Unlike in...
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Log-concavity and log-convexity of series containing multiple Pochhammer symbols
In this paper, we study power series with coefficients equal to a product of a generic sequence and an explicitly given function of a positive...
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Dynamical implications of convexity beyond dynamical convexity
We establish sharp dynamical implications of convexity on symmetric spheres that do not follow from dynamical convexity. It allows us to show the...
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The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation
A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan formula expressing the...
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Some calculus rules, generalized convexity via convexifactors and their applications
In this paper, convexifactors of product and quotient of functions are computed. Generalized convexity of these functions in terms of convexifactors...
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Convexity and its Applications
This chapter is devoted to several applications of convexity other than the semicontinuity of integral functionals that we already saw in Chap....
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Power Convexity of Solutions to a Special Lagrangian Equation in Dimension Two
In this paper, we prove power convexity result of solution to Dirichlet problem of special Lagrangian equation in dimension two. This provides new...
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1-Dimensional Topological Invariants to Estimate Loss Surface Non-Convexity
AbstractWe utilize the framework of topological data analysis to examine the geometry of loss landscape. With the use of topology and Morse theory,...
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A new class of fractional inequalities through the convexity concept and enlarged Riemann–Liouville integrals
Fractional inequalities play a crucial role in building mathematical mechanisms and their related solution functions across the majority of practical...
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Variational Convexity of Functions in Banach Spaces
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has...
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Diamond-Alpha Pachpatte Type Dynamic Inequalities Via Convexity
Diamond-alpha Pachpatte type dynamic inequalities, which are convex generalizations of diamond-alpha Hardy−Copson type inequalities, are established...
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Regularity in shape optimization under convexity constraint
This paper is concerned with the regularity of shape optimizers of a class of isoperimetric problems under convexity constraint. We prove that...
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On Some Operator Inequalities with Respect to the s-Convexity
In this paper, we extend the concept of s -convexity from the case where the functions are with real variables to the case where the functions are...