Results 11 to 20 of about 482,837 (303)
Modulus of convexity for operator convex functions [PDF]
Journal of Mathematical Physics, 2014 Given an operator convex function f(x), we obtain an operator-valued lower bound for cf(x) + (1 − c)f(y) − f(cx + (1 − c)y), c ∈ [0, 1]. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false for functions that are convex but not operator convex.
Kim, Isaac H.
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A Characterization of Convex Functions [PDF]
The American Mathematical Monthly, 2018 Let $D$ be a convex subset of a real vector space. It is shown that a radially lower semicontinuous function $f: D\to \mathbf{R}\cup \{+\infty\}$ is convex if and only if for all $x,y \in D$ there exists $ = (x,y) \in (0,1)$ such that $f( x+(1- )y) \le f(x)+(1- )f(y)$.
Leonetti, Paolo
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Valuations on Convex Functions [PDF]
International Mathematics Research Notices, 2017 All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.
Andrea Colesanti +2 more
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Schur-Convexity of Averages of Convex Functions [PDF]
Journal of Inequalities and Applications, 2011 The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasi-arithmetic mean is studied.
Roqia Ghulam +3 more
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Radical Convex Functions [PDF]
Mediterranean Journal of Mathematics, 2021 to appear in Mediterr.
Mohammad Sababheh, Hamid Reza Moradi
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Smooth convex extensions of convex functions [PDF]
Calculus of Variations and Partial Differential Equations, 2019 Final ...
Azagra, Daniel, Mudarra, Carlos
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Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind.
Ali Hassan +3 more
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Strongly convex functions, Moreau envelopes and the generic nature of convex functions with strong minimizers [PDF]
, 2015 In this work, using Moreau envelopes, we define a complete metric for the set of proper lower semicontinuous convex functions. Under this metric, the convergence of each sequence of convex functions is epi-convergence.
Planiden, Chayne, Wang, Xianfu
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On φ-convexity of convex functions
Linear Algebra and its Applications, 1998 AbstractWe construct a non-trivial set φ of extended-real valued functions on Rn, containing all affine functions, such that an extended-real valued function f on Rn is convex if and only if it is φ-convex in the sense of Dolecki and Kurcyusz, i.e., the (pointwise) supremum of some subset of φ. Also, we prove a new sandwich theorem.
Ivan Singer +1 more
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On the singularities of convex functions [PDF]
Manuscripta Mathematica, 1992 Given a semi-convex functionu: ω⊂R n→R and an integerk≡[0,1,n], we show that the set ∑k defined by $$\Sigma ^k = \left\{ {x \in \Omega :dim\left( {\partial u\left( x \right)} \right) \geqslant k} \right\}$$ is countably ℋn-k i.e., it is ...
Alberti G, AMBROSIO, Luigi, Cannarsa P.
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