scholarly journals Interpolating Jensen-type operator inequalities for log-convex and superquadratic functions

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4523-4535
Author(s):  
Mojtaba Bakherad ◽  
Mohsen Kian ◽  
Mario Krnic ◽  
Seyyed Ahmadi
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Operator ◽  
Operator Inequality ◽  
Operator Inequalities ◽  
Superquadratic Functions

Motivated by some recently established Jensen-type operator inequalities related to a convex function, in the present paper we derive several more accurate Jensen-type operator inequalities for certain subclasses of convex functions. More precisely, we obtain interpolating series of Jensen-type inequalities utilizing log-convex and non-negative superquadratic functions. In particular, we obtain the corresponding refinements of the Jensen-Mercer operator inequality for such classes of functions.

scholarly journals External Jensen-type operator inequalities via superquadraticity

2020 ◽  
pp. 31-31
Author(s):  
Mohsen Kian ◽  
Mario Krnic ◽  
Mohsen Delavar
Keyword(s):  
Type Operator ◽  
Jensen Inequality ◽  
Operator Inequalities ◽  
Superquadratic Functions ◽  
Adjoint Operators ◽  
External Form

In this paper we establish several Jensen-type operator inequalities for a class of superquadratic functions and self-adjoint operators. Our results are given in the so-called external form. As an application, we give improvements of the H?lder?McCarthy inequality and the classical discrete and integral Jensen inequality in the corresponding external forms. In addition, the established Jensen-type inequalities are compared with the previously known results and we show that our results provide more accurate estimates in some general settings.

scholarly journals On Generalized Strongly Convex Functions and Unified Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Timing Yu ◽  
Ghulam Farid ◽  
Kahkashan Mahreen ◽  
Chahn Yong Jung ◽  
Soo Hak Shim
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Operator Inequalities ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Left And Right

In this paper, we define a strongly exponentially α , h − m -convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature.

scholarly journals Operator inequalities of Jensen type

2013 ◽  
Vol 1 ◽  
pp. 9-21
Author(s):  
M. S. Moslehian ◽  
J. Mićić ◽  
M. Kian
Keyword(s):  
Convex Function ◽  
Type Operator ◽  
Operator Inequalities ◽  
Continuous Convex Function ◽  
Adjoint Operators

Abstract We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, thenfor all operators Ci such that (i=1 , ... , n) for some scalar M ≥ 0, where and

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 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.

Continuity of h-convex functions

2019 ◽  
Vol 12 (04) ◽  
pp. 1950059
Author(s):  
M. Rostamian Delavar ◽  
S. S. Dragomir
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Continuity Condition

In this paper, a condition which implies the continuity of an [Formula: see text]-convex function is investigated. In fact, any [Formula: see text]-convex function bounded from above is continuous if the function [Formula: see text] satisfies a certain condition which is called pre-continuity condition.

scholarly journals Conformable Fractional Integrals Versions of Hermite-Hadamard Inequalities and Their Generalizations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Gohar Ali
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integrals ◽  
Montgomery Identity

We prove new Hermite-Hadamard inequalities for conformable fractional integrals by using convex function, s-convex, and coordinate convex functions. We prove new Montgomery identity and by using this identity we obtain generalized Hermite-Hadamard type inequalities.

scholarly journals On Ostrowski-Mercer inequalities for differentiable convex function

2021 ◽  
Author(s):  
Muhammad Aamir Ali ◽  
Ifra Bashir Sial ◽  
Hüseyin BUDAK
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Ostrowski Inequality ◽  
Special Means

In this note, for differentiable convex functions, we prove some new Ostrowski-Mercer inequalities. These inequalities generalize an Ostrowski inequality and related inequalities proved in [3,5]. Some applications to special means are also given.

scholarly journals On the Hermite-Hadamard inequalities for h-convex functions on balls and ellipsoids

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5871-5886
Author(s):  
Xiaoqian Wang ◽  
Jianmiao Ruan ◽  
Xinsheng Ma
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
High Dimensional

In this paper, we establish some Hermite-Hadamard type inequalities for h- convex function on high-dimensional balls and ellipsoids, which extend some known results. Some mappings connected with these inequalities and related results are also obtained.

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