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.

Exponential trigonometric convex functions and Hermite-Hadamard type inequalities

2021 ◽  
Vol 71 (1) ◽  
pp. 43-56
Author(s):  
Mahir Kadakal ◽  
İmdat İşcan ◽  
Praveen Agarwal ◽  
Mohamed Jleli
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Power Mean ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
First Derivative ◽  
Algebraic Properties ◽  
Class Of Functions

Abstract In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.

scholarly journals Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saad Ihsan Butt ◽  
Artion Kashuri ◽  
Muhammad Tariq ◽  
Jamshed Nasir ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Convex Function ◽  
Error Estimates ◽  
Exponential Type ◽  
Convex Functions ◽  
Type Inequality ◽  
Hadamard Inequality ◽  
Absolute Value ◽  
Special Means ◽  
Algebraic Properties

Abstract In this paper, we give and study the concept of n-polynomial $(s,m)$ ( s , m ) -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial $(s,m)$ ( s , m ) -exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at certain power are n-polynomial $(s,m)$ ( s , m ) -exponential-type convex. Some applications to special means and new error estimates for the trapezoid formula are given.

Relative h-preinvex functions and integral inequalities

2020 ◽  
Vol 27 (2) ◽  
pp. 285-295
Author(s):  
Marian Matłoka
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
New Class ◽  
Preinvex Functions ◽  
New Inequalities

AbstractIn this paper, we consider a new class of convex functions, called relative h-preivex functions. Seven new inequalities of Hermite–Hadamard type for relative h-preinvex functions are established using different approaches.

scholarly journals Some integral inequalities for generalized preinvex functions with applications

2021 ◽  
Vol 6 (12) ◽  
pp. 13907-13930
Author(s):  
Muhammad Tariq ◽  
◽  
Soubhagya Kumar Sahoo ◽  
Fahd Jarad ◽  
Bibhakar Kodamasingh ◽  
...  
Keyword(s):  
Type Inequality ◽  
Additional Research ◽  
Integral Inequalities ◽  
The Novel ◽  
Special Cases ◽  
Algebraic Properties ◽  
Preinvex Functions ◽  
Harmonic Means ◽  
New Inequalities

<abstract><p>The main objective of this work is to explore and characterize the idea of $ s $-type preinvex function and related inequalities. Some interesting algebraic properties and logical examples are given to support the newly introduced idea. In addition, we attain the novel version of Hermite-Hadamard type inequality utilizing the introduced preinvexity. Furthermore, we establish two new identities, and employing these, we present some refinements of Hermite-Hadamard-type inequality. Some special cases of the presented results for different preinvex functions are deduced as well. Finally, as applications, some new inequalities for the arithmetic, geometric and harmonic means are established. Results obtained in this paper can be viewed as a significant improvement of previously known results. The awe-inspiring concepts and formidable tools of this paper may invigorate and revitalize for additional research in this worthy and absorbing field.</p></abstract>

scholarly journals On n-polynomial p-convex functions and some related inequalities

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
Yu-Ming Chu ◽  
Muhammad Shoaib Saleem ◽  
Nazia Jahangir ◽  
Nasir Rehman
Keyword(s):  
Convex Functions ◽  
New Class ◽  
Algebraic Properties

AbstractIn this paper, we introduce a new class of convex functions, so-called n-polynomial p-convex functions. We discuss some algebraic properties and present Hermite–Hadamard type inequalities for this generalization. Moreover, we establish some refinements of Hermite–Hadamard type inequalities for this new class.

scholarly journals A Class of SemilocalE-Preinvex Functions and Its Applications in Nonlinear Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hehua Jiao ◽  
Sanyang Liu ◽  
Xinying Pai
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions ◽  
Convex Set ◽  
Basic Properties ◽  
New Class ◽  
Duality Results ◽  
Invex Set ◽  
Preinvex Functions ◽  
Class Of Functions

A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

scholarly journals On exponentially ϱ-preinvex functions and associated trapezium like inequalities

2021 ◽  
pp. 25-25
Author(s):  
Artion Kashuri ◽  
Muhammad Awan ◽  
Sadia Talib ◽  
Muhammad Noor ◽  
Khalida Noor
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions

In this paper, authors introduce a new extension of ?-convexity called ?- preinvexity and generalize the discussed results by Wu et al. in ?On a new class of convex functions and integral inequalities?. Some special cases are deduced from main results. At the end, a briefly conclusion is given.

scholarly journals Simpson type inequalities and applications

2021 ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Michael Th. Rassias ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Quadrature Formula ◽  
Convex Functions ◽  
Integral Identity ◽  
Higher Order ◽  
Auxiliary Result ◽  
First Order ◽  
New Class ◽  
Differentiable Functions

AbstractA new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of $$\sigma >0$$ σ > 0 . We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

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