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Converse Ohlin’s lemma for convex and strongly convex functions
Journal of Applied Analysis, 2022Abstract Theorems which are converse to the Ohlin lemma for convex and strongly convex functions are proved. New proofs of probabilistic characterizations of convex and strongly convex functions are presented.
Mirosław Adamek, Kazimierz Nikodem
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Some Remarks on Close-to-Convex and Strongly Convex Functions [PDF]
MATHEMATICA SCANDINAVICA, 2015 We consider questions of the following kind: When does boundedness of $|{\arg \{1+zp'(z)/p(z)\}}|$, for a given analytic function $p$, imply boundedness of $|{\arg\{p(z)\}}|$? The paper determines the order of strong close-to-convexity in the class of strongly convex functions.
M. Nunokawa +2 more
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Strongly E-convex sets and strongly E-convex functions
Journal of Interdisciplinary Mathematics, 2005Abstract A class of E-convex sets and a class of E-convex functions are extended to the so called strongly E-convex sets and strongly E-convex functions. In this extension we take into account the images of two points x and y under an E : Rn → Rn operator besides the two points themselves.
T Emam
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Remarks on strongly convex functions
Aequationes Mathematicae, 2010Let \(I\subseteq \mathbb{R}\) be an interval and \(c\) be a positive number. A function \(f:I\rightarrow \mathbb{R}\) is called strongly convex with modulus \( c\) if \[ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-ct(1-t)(x-y)^{2}, \] for all \(x,y\in I\) and \(t\in [0,1]\).
Kazimierz Nikodem +2 more
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Strongly log-Convex Functions [PDF]
Information Sciences Letters, 2021 Some new concepts of the strongly log convex functions are considered in this paper. Properties of the strongly convex functions are investigated under suitable conditions.
Aslam Noor, Muhammad +1 more
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The concept of coordinate strongly convex functions and related inequalities
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2018Muhammad Adil Khan +2 more
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On Generalized Strongly Convex Functions Involving Bifunction [PDF]
Applied Mathematics & Information Sciences, 2019 In this paper, we define and introduce some new concepts of the generalized strongly convex functions and generalized strongly monotone operators with respect to an arbitrary non-negative bifunction.
Muhammad Aslam, Khalida Inayat Noor, Noor
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\(C^2\)-Lusin approximation of strongly convex functions [PDF]
Given a strongly convex function mapping from a Euclidean space to the real one, the authors show that for any \(\varepsilon > 0\), there exists a \(C^2\) strongly convex function that is a Lusin-type approximation of the initial one such that the \(\ell^{\infty}\)-norm of the difference of these functions is less than \(\varepsilon\).
Azagra, Daniel +2 more
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On strongly convex sets and strongly convex functions
Journal of Mathematical Sciences, 2000The basic notions of this paper are generating set and \(M\)-strongly convex set, which have grown from the axiomatic approach to the notion of convexity. A convex closed set \(M\) of a Banach space \(E\) is called a generating set if for any nonempty set \(A\) of the form \(A=\bigcap_{x\in X}(M+x)\) one can find a convex closed set \(B\subset E\) such
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On the properties of strongly hd convex functions
Annals of the University of Craiova Mathematics and Computer Science SeriesWe study some optimization properties of $h_d$ strongly convex functions. More precisely, we discuss the characterization properties/inequalities (existence and uniqueness) of minima of $h_d$ strongly convex functions. Moreover, connections with polynomial norms are also presented.
Lăchescu Geanina-Maria +1 more
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