scholarly journals Strong h-Convexity and Separation Theorems

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Teodoro Lara ◽  
Nelson Merentes ◽  
Kazimierz Nikodem
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Stability Result ◽  
Jensen Inequality ◽  
Separation Theorems

Jensen inequality for strongly h-convex functions and a characterization of pairs of functions that can be separated by a strongly h-convex function are presented. As a consequence, a stability result of the Hyers-Ulam type is obtained.

scholarly journals Sandwich theorem for reciprocally strongly convex functions

2018 ◽  
Vol 52 (2) ◽  
pp. 171-184
Author(s):  
Mireya Bracamonte ◽  
José Giménez ◽  
Jesús Medina
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Stability Result ◽  
Real Interval ◽  
Strongly Convex Functions ◽  
Strongly Convex Function ◽  
Strongly Convex ◽  
Sandwich Theorem ◽  
Approximate Convexity ◽  
Class Of Functions

We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.

Generalization of cyclic refinements of Jensen inequality by montgomery identity and Green’s function

2018 ◽  
Vol 11 (04) ◽  
pp. 1850060 ◽  
Author(s):  
Nasir Mehmood ◽  
Saad Ihsan Butt ◽  
Josip Pečarić
Keyword(s):  
Convex Function ◽  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Mean Value ◽  
Higher Order ◽  
Jensen Inequality ◽  
Linear Functionals ◽  
Montgomery Identity ◽  
Exponential Convexity

We consider discrete and continuous cyclic refinements of Jensen’s inequality and generalize them from convex function to higher order convex function by means of Lagrange Green’s function and Montgomery identity. We give application of our results by formulating the monotonicity of the linear functionals obtained from generalized identities utilizing the theory of inequalities for [Formula: see text]-convex functions at a point. We compute Grüss and Ostrowski type bounds for generalized identities associated with the obtained inequalities. Finally, we investigate the properties of linear functionals regarding exponential convexity log convexity and mean value theorems.

scholarly journals Integral Inequalities Involving Strongly Convex Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Ying-Qing Song ◽  
Muhammad Adil Khan ◽  
Syed Zaheer Ullah ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Jensen Inequality ◽  
Jensen's Inequality ◽  
Strongly Convex Functions ◽  
Strongly Convex Function ◽  
Strongly Convex

We study the notions of strongly convex function as well as F-strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of companion inequality to Jensen’s inequality established by Matić and Pečarić is shown to be recaptured as a particular instance. Counterpart of the integral Jensen inequality for strongly convex functions is also presented. Furthermore, we present integral Jensen-Steffensen and Slater’s inequality for strongly convex functions.

Some properties of convex functions

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 3015-3021
Author(s):  
Miloljub Albijanic
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Real Variable ◽  
First Derivative ◽  
Upper Limit ◽  
Definition Of

We treat two problems on convex functions of one real variable. The first one is concerned with properties of tangent lines to the graph of a convex function and essentially is related to the questions on the first derivative (if it exists). The second problem is related to Schwarz?s derivative, in fact its upper limit modification. It gives an interesting characterization of convex functions. Let us recall the definition of a convex functions.

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.

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