scholarly journals A Formula on the Conjugate of the Max of a Convex Function and a Concave Function

1998 ◽  
Vol 220 (1) ◽  
pp. 313-321 ◽  
Author(s):  
Michel Volle
Keyword(s):  
Convex Function ◽  
Concave Function

scholarly journals SOME RESULTS RELATED TO CONVEXIFIABLE FUNCTIONS

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Faraz Mehmood
Keyword(s):  
Convex Function ◽  
Present Article ◽  
Concave Function

The present article is devoted to the class of convexifiable functions and related results. In this way, we would recapture the result of authors L. Maligranda et. al. and we would obtain new majorization type results for weighted convexifiable function. This article also recaptures similar results for convex function as well as for concave function

scholarly journals A duality theorem for a nondifferentiable nonlinear fractional programming problem

1979 ◽  
Vol 20 (3) ◽  
pp. 397-406 ◽  
Author(s):  
B. Mond ◽  
B.D. Craven
Keyword(s):  
Convex Function ◽  
Objective Function ◽  
Fractional Programming ◽  
Support Function ◽  
Duality Theorem ◽  
Convex Set ◽  
Concave Function ◽  
Special Cases ◽  
Nonlinear Fractional Programming ◽  
Converse Duality Theorem

A duality theorem, and a converse duality theorem, are proved for a nonlinear fractional program, where the numerator of the objective function involves a concave function, not necessarily differentiable, and also the support function of a convex set, and the denominator involves a convex function, and the support function of a convex set. Various known results are deduced as special cases.

scholarly journals Petrović-Type Inequalities for Harmonic h-convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Imran Abbas Baloch ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Multiplicative Function ◽  
Concave Function ◽  
Monotonicity Properties ◽  
Harmonic Convex

In the article, we establish several Petrović-type inequalities for the harmonic h-convex (concave) function if h is a submultiplicative (super-multiplicative) function, provide some new majorizaton type inequalities for harmonic convex function, and prove the superadditivity, subadditivity, linearity, and monotonicity properties for the functionals derived from the Petrović type inequalities.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

scholarly journals On Certain Differential Subordination of Harmonic Mean Related to a Linear Function

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 966
Author(s):  
Anna Dobosz ◽  
Piotr Jastrzębski ◽  
Adam Lecko
Keyword(s):  
Convex Function ◽  
Linear Function ◽  
Differential Subordination ◽  
Harmonic Mean ◽  
Best Dominant ◽  
Symmetry Properties ◽  
Differential Subordinations ◽  
Difficult Issue

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

scholarly journals Estimation of different entropies via Lidstone polynomial using Jensen-type functionals

2020 ◽  
Vol 9 (3) ◽  
pp. 613-631
Author(s):  
Khuram Ali Khan ◽  
Tasadduq Niaz ◽  
Đilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Function ◽  
Shannon Entropy ◽  
Rényi Divergence ◽  
Lidstone Polynomial

Abstract In this work, some new functional of Jensen-type inequalities are constructed using Shannon entropy, f-divergence, and Rényi divergence, and some estimates are obtained for these new functionals. Also using the Zipf–Mandelbrot law and hybrid Zipf–Mandelbrot law, we investigate some bounds for these new functionals. Furthermore, we generalize these new functionals for m-convex function using Lidstone polynomial.

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