scholarly journals Hermite-Hadamard-Type Inequalities forr-Preinvex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wasim Ul-Haq ◽  
Javed Iqbal
Keyword(s):  
Hadamard Inequality ◽  
Preinvex Functions

We aim to fi…nd Hermite-Hadamard inequality forr-preinvex functions. Also, it is investigated for the product of anr-preinvex function ands-preinvex function.

EXTENSIONS OF THE HERMITE–HADAMARD INEQUALITY FOR -PREINVEX FUNCTIONS ON AN INVEX SET

2017 ◽  
Vol 95 (3) ◽  
pp. 412-423 ◽  
Author(s):  
DAH-YAN HWANG ◽  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hadamard Inequality ◽  
Invex Set ◽  
Preinvex Functions ◽  
Necessary And Sufficient

Necessary and sufficient conditions to characterise weakly $r$-preinvex functions on an invex set are obtained and used to establish generalisations of the Hermite–Hadamard inequality for such functions.

scholarly journals A Comprehensive Analysis of Hermite–Hadamard Type Inequalities via Generalized Preinvex Functions

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 328
Author(s):  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Hüseyin Budak ◽  
Soubhagya Kumar Sahoo ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Convex Functions ◽  
Comprehensive Analysis ◽  
Additional Research ◽  
Hadamard Inequality ◽  
New Class ◽  
Principal Objective ◽  
New Variant ◽  
Algebraic Properties ◽  
Preinvex Functions ◽  
Insight Into

The principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known Hermite–Hadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field.

scholarly journals Hermite-Hadamard-Fejér Inequalities for Conformable Fractional Integrals via Preinvex Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yousaf Khurshid ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu ◽  
Zareen Abdulhameed Khan
Keyword(s):  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Right Hand ◽  
Fejér Inequality ◽  
Preinvex Functions ◽  
The Right

In this paper, we present a Hermite-Hadamard-Fejér inequality for conformable fractional integrals by using symmetric preinvex functions. We also establish an identity associated with the right hand side of Hermite-Hadamard inequality for preinvex functions; then by using this identity and preinvexity of functions and some well-known inequalities, we find several new Hermite-Hadamard type inequalities for conformal fractional integrals.

scholarly journals Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nidhi Sharma ◽  
Sanjeev Kumar Singh ◽  
Shashi Kant Mishra ◽  
Abdelouahed Hamdi
Keyword(s):  
Fractional Integrals ◽  
Hadamard Inequality ◽  
Interval Valued Function ◽  
Preinvex Functions ◽  
Theoretical Results ◽  
Interval Valued

AbstractIn this paper, we introduce $(h_{1},h_{2})$ ( h 1 , h 2 ) -preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.

scholarly journals A new q-integral identity and estimation of its bounds involving generalized exponentially μ-preinvex functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Differentiable Function ◽  
Integral Identity ◽  
Second Order ◽  
Integral Inequalities ◽  
Absolute Value ◽  
Type Integral ◽  
Preinvex Functions

Abstract In the article, we introduce the generalized exponentially μ-preinvex function, derive a new q-integral identity for second order q-differentiable function, and establish several new q-trapezoidal type integral inequalities for the function whose absolute value of second q-derivative is exponentially μ-preinvex.

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.

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