scholarly journals Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Ali Barani ◽  
Amir G Ghazanfari ◽  
Sever S Dragomir
Keyword(s):  
Hadamard Inequality

On a certain stability of the Hermite–Hadamard inequality

2008 ◽  
Vol 465 (2102) ◽  
pp. 571-583 ◽  
Author(s):  
Attila Házy ◽  
Zsolt Páles
Keyword(s):  
Functional Inequalities ◽  
Hadamard Inequality ◽  
Real Functions ◽  
The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

scholarly journals New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1108 ◽  
Author(s):  
Juan E. Nápoles Valdés ◽  
José M. Rodríguez ◽  
José M. Sigarreta
Keyword(s):  
Integral Operators ◽  
Hadamard Inequality ◽  
Applied Development

At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators.

scholarly journals Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
Miguel J. Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Quantum Calculation ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Quantum Integral

In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

scholarly journals Some Properties and Inequalities for the h,s-Nonconvex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chengli Wang ◽  
Muhammad Shoaib Saleem ◽  
Hamood Ur Rehman ◽  
Muhammad Imran
Keyword(s):  
Jensen Inequality ◽  
Weighted Version ◽  
Hadamard Inequality ◽  
Basic Properties ◽  
Nonconvex Functions ◽  
Schur Inequality ◽  
Class Of Functions

The purpose of this paper is to introduce the notion of strongly h,s-nonconvex functions and to present some basic properties of this class of functions. We present Schur inequality, Jensen inequality, Hermite–Hadamard inequality, and weighted version of the Hermite–Hadamard inequality.

scholarly journals On q-Hermite-Hadamard Inequalities for Differentiable Convex Functions

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 632 ◽  
Author(s):  
Seksan Jhanthanam ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Kamsing Nonlaopon
Keyword(s):  
Critical Point ◽  
Convex Functions ◽  
Hadamard Inequality ◽  
Left Hand ◽  
Point Type

In this paper, we establish some new results on the left-hand side of the q-Hermite–Hadamard inequality for differentiable convex functions with a critical point. Our work extends the results of Alp et. al (q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci., 2018, 30, 193-203), by considering the critical point-type inequalities.

scholarly journals Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 117
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge Eliecer Hernández Hernández
Keyword(s):  
Convex Functions ◽  
Special Function ◽  
Fractional Integrals ◽  
Generalized Convex Functions ◽  
Hadamard Inequality ◽  
Trapezium Type ◽  
Several Variables ◽  
Special Cases ◽  
Interesting Identity ◽  
Generalized Coordinate

In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

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