Results 11 to 20 of about 10,963,226 (321)
New Hermite–Hadamard type inequalities for n-polynomial harmonically convex functions
Journal of Inequalities and Applications, 2020 In the article, we introduce a class of n-polynomial harmonically convex functions, establish their several new Hermite–Hadamard type inequalities which are the generalizations and variants of the previously known results for harmonically convex ...
M. U. Awan +4 more
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On the singularities of convex functions [PDF]
Manuscripta Mathematica, 1992 A rectifiability result is provided for the singular sets of convex and semiconvex functions. In fact, for every real convex or semiconvex function \(u\) on a convex open subset \(\Omega\) of \({\mathbf R}^ n\), and every integer \(k\) such that \(0< k\leq n\), one may consider the set \(\Sigma^ k\) of all points \(x\in\Omega\) such that the ...
Alberti G, AMBROSIO, Luigi, Cannarsa P.
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The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functions
SIAM Journal on Optimization, 2020 The boosted difference of convex functions algorithm (BDCA) was recently proposed for minimizing smooth difference of convex (DC) functions.
F. J. A. Artacho, P. Vuong
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On Caputo fractional derivatives via exponential \(s,m\)-convex functions
Engineering and Applied Science Letters, 2020 In this paper, we establish several integral inequalities including Caputo fractional derivatives for exponential \(s,m\)-convex functions. By using convexity for exponential \(s,m\)-convex functions of any positive integer order differentiable function ...
G. Farid, M. Nadeem, S. Butt
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Convex Defining Functions for Convex Domains [PDF]
Journal of Geometric Analysis, 2010 21 ...
Jeffery D. McNeal, A. K. Herbig
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New Hermite-Hadamard type inequalities for exponentially convex functions and applications
AIMS Mathematics, 2020 The investigation of the proposed techniques is effective and convenient for solving the integrodifferential and difference equations. The present investigation depends on two highlights; the novel Hermite-Hadamard type inequalities for $\mathcal{K ...
Shuang-Shuang Zhou +5 more
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Continued fractions built from convex sets and convex functions [PDF]
, 2014 In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions with deterministic terms are provided.
Molchanov, Ilya
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On φ-convexity of convex functions
Linear Algebra and its Applications, 1998 The authors construct a non-trivial set \(\Phi\) of extended-real valued functions on \(R^n\) containing all affine functions, such that an extended-real valued function defined on \(R^n\) is convex if and only if it is \(\Phi\)-convex, i.e., it is the pointwise supremum of some subset of \(\Phi\). They also prove a new sandwich theorem.
Ivan Singer +1 more
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2D approximately reciprocal ρ-convex functions and associated integral inequalities
, 2020 The main objective of this article is to introduce the notion of 2D approximately reciprocal ρ-convex functions, show that this class of functions unifies several other unrelated classes of reciprocal convex functions, obtain several new refinements of ...
M. U. Awan +4 more
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Approximately convex functions [PDF]
Proceedings of the American Mathematical Society, 1952 So far we have discussed the stability of various functional equations. In the present section, we consider the stability of a well-known functional inequality, namely the inequality defining convex functions: $$f\left( {\lambda x + \left( {1 - \lambda } \right)y} \right) \leqslant \lambda f\left( x \right) + \left( {1 - \lambda } \right)f\left( y \
Stanislaw M. Ulam, Donald H. Hyers
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