scholarly journals A generalization of Hadamard’s inequality for convex functions

2008 ◽  
Vol 21 (3) ◽  
pp. 254-257 ◽  
Author(s):  
W.H. Yang
Keyword(s):  
Convex Functions ◽  
Hadamard’S Inequality

scholarly journals ON QUASI CONVEX FUNCTIONS AND HADAMARD'S INEQUALITY

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
K.-L. Tseng ◽  
G.-S. Yang ◽  
S. S. Dragomir
Keyword(s):  
Convex Functions ◽  
Hadamard’S Inequality

scholarly journals Quasi-convex functions and Hadamard's inequality

1998 ◽  
Vol 57 (3) ◽  
pp. 377-385 ◽  
Author(s):  
S.S. Dragomir ◽  
C.E.M. Pearce
Keyword(s):  
Convex Functions ◽  
Hadamard’S Inequality ◽  
Quasi Convexity

Some extensions of quasi-convexity appearing in the literature are explored and relations found between them. Hadamard's inequality is connected tenaciously with convexity and versions of it are shown to hold in our setting. Our theorems extend and unify a number of known results. In particular, we derive a generalised Kenyon-Klee theorem.

scholarly journals On Certain Properties for Two Classes of Generalized Convex Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed S. S. Ali
Keyword(s):  
Convex Functions ◽  
Generalized Convexity ◽  
Generalized Convex Functions ◽  
Hadamard’S Inequality ◽  
Extremum Property

Two classes of generalized convex functions in the sense of Beckenbach are considered. For both classes, we show that the existence of support curves implies their generalized convexity and obtain an extremum property of these functions. Furthermore, we establish Hadamard’s inequality for them.

scholarly journals Generalizations of Hermite–Hadamard like inequalities involving $\chi _{{\kappa }}$-Hilfer fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yu-Ming Chu ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Hadamard’S Inequality ◽  
Integral Identities

Abstract The main objective of this paper is to obtain a new κ-fractional analogue of Hermite–Hadamard’s inequality using the class of s-convex functions and $\chi _{{\kappa }}$ χ κ -Hilfer fractional integrals. In order to obtain other main results of the paper we derive two new fractional integral identities using the definitions of $\chi _{{\kappa }}$ χ κ -Hilfer fractional integrals. For the validity of these identities we also take some particular examples. Using these identities we then obtain some more new variants of Hermite–Hadamard’s inequality using s-convex functions.

scholarly journals Generalized Convex Functions on Fractal Sets and Two Related Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Huixia Mo ◽  
Xin Sui ◽  
Dongyan Yu
Keyword(s):  
Convex Function ◽  
Real Line ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Generalized Convex Functions ◽  
Fractal Sets ◽  
Hadamard’S Inequality

We introduce the generalized convex function on fractal setsRα  (0<α≤1)of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen’s inequality and generalized Hermite-Hadamard's inequality. Furthermore, some applications are given.

Refinements to Hadamard’s Inequality for r-Convex Functions

2010 ◽  
Author(s):  
W. T. Sulaiman ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Convex Functions ◽  
Hadamard’S Inequality

scholarly journals A Study of Uniform Harmonic χ -Convex Functions with respect to Hermite-Hadamard’s Inequality and Its Caputo-Fabrizio Fractional Analogue and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Miguel Vivas-Cortez ◽  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Hadamard’S Inequality ◽  
Special Cases ◽  
Harmonic Convex

In this paper, we introduce the notion of uniform harmonic χ -convex functions. We show that this class relates several other unrelated classes of uniform harmonic convex functions. We derive a new version of Hermite-Hadamard’s inequality and its fractional analogue. We also derive a new fractional integral identity using Caputo-Fabrizio fractional integrals. Utilizing this integral identity as an auxiliary result, we obtain new fractional Dragomir-Agarwal type of inequalities involving differentiable uniform harmonic χ -convex functions. We discuss numerous new special cases which show that our results are quite unifying. Finally, in order to show the significance of the main results, we discuss some applications to means of positive real numbers.

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