Errors of gradient extrema of a strictly convex function of discrete argument

1992 ◽  
Vol 2 (2) ◽  
Author(s):  
V. A. EMELICHEV ◽  
M. M. KOVALEV ◽  
A. B. RAMAZANOV
Keyword(s):  
Convex Function ◽  
Strictly Convex ◽  
Discrete Argument

scholarly journals A note on convex functions

1999 ◽  
Vol 22 (3) ◽  
pp. 525-534 ◽  
Author(s):  
Yu-Ru Syau
Keyword(s):  
Continuous Function ◽  
Euclidean Space ◽  
Convex Function ◽  
Convex Functions ◽  
Dimensional Euclidean Space ◽  
Strictly Convex ◽  
Lower Semi

In this paper, we give two weak conditions for a lower semi-continuous function on then-dimensional Euclidean spaceRnto be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.

scholarly journals Extension of The Best Approximation Operator in Orlicz Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Ivana Carrizo ◽  
Sergio Favier ◽  
Felipe Zó
Keyword(s):  
Convex Function ◽  
Orlicz Space ◽  
Best Approximation ◽  
Probability Space ◽  
Orlicz Spaces ◽  
Approximation Operator ◽  
Strictly Convex ◽  
The Best Approximation ◽  
Convergence Results

Let(Ω,𝒜,μ)be a probability space andℒ⊂𝒜a sub-σ-lattice of theσ-algebra𝒜. We study an extension of the bestϕ-approximation operator from an Orlicz spaceLϕto the spaceLϕ′, whereϕ′denotes the derivative of the convex, but not necessarily a strictly convex functionϕ. We obtain convergence results when a sequence ofσ-algebrasℬnconverges toℬ∞in a suitable way.

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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