scholarly journals Ostrowski type inequalities involving conformable integrals via preinvex functions

AIP Advances ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 055204 ◽  
Author(s):  
Yousaf Khurshid ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Preinvex Functions

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.

scholarly journals Some Hermite-Hadamard type integral inequalities for operator AG-preinvex functions

2016 ◽  
Vol 8 (2) ◽  
pp. 312-323
Author(s):  
Ali Taghavi ◽  
Haji Mohammad Nazari ◽  
Vahid Darvish
Keyword(s):  
Integral Inequalities ◽  
Unitarily Invariant Norm ◽  
Norm Inequalities ◽  
Invariant Norm ◽  
Type Integral ◽  
Preinvex Functions ◽  
Inequalities For Operators

Abstract In this paper, we introduce the concept of operator AG-preinvex functions and prove some Hermite-Hadamard type inequalities for these functions. As application, we obtain some unitarily invariant norm inequalities for operators.

scholarly journals New Integral Inequalities via Generalized Preinvex Functions

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 296
Author(s):  
Muhammad Tariq ◽  
Asif Ali Shaikh ◽  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Power Mean ◽  
Science And Engineering ◽  
Special Means ◽  
Algebraic Properties ◽  
Convexity Theory ◽  
Hölder’S Integral Inequality ◽  
Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

scholarly journals Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

scholarly journals SOME PROPERTIES OF EXPONENTIALLY PREINVEX FUNCTIONS

2019 ◽  
pp. 941
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Optimality Conditions ◽  
Convex Functions ◽  
New Concepts ◽  
Preinvex Functions

In this paper, we introduce some new concepts of the exponentially preinvex functions. We investigate several properties of the exponentially preinvex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational-like inequalities. Several interesting results characterizing the exponentially preinvex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results.

scholarly journals Some New Postquantum Integral Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yu-Ming Chu ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Sabah Iftikhar ◽  
Latifa Riahi
Keyword(s):  
Integral Identity ◽  
Integral Inequalities ◽  
Auxiliary Result ◽  
Special Cases ◽  
Preinvex Functions

The goal of this paper is to derive a new generalized postquantum integral identity. Using this new identity as an auxiliary result, we derive some new variants of integral inequalities using p , q -differentiable preinvex functions. We also point out some special cases of the obtained results which show that our results are quite unifying ones.

scholarly journals Generalized Preinvex Functions and Their Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 493 ◽  
Author(s):  
Adem Kiliçman ◽  
Wedad Saleh
Keyword(s):  
Sufficient Conditions ◽  
Basic Properties ◽  
Preinvex Functions ◽  
Constrained Programming ◽  
New Inequalities

A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality constrained programming are discussed under the sub-b-s-preinvexity. Moreover, some new inequalities of the Hermite—Hadamard type for differentiable sub-b-s-preinvex functions are presented. Examples of applications of these inequalities are shown.

scholarly journals Some New q—Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 553 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Artion Kashuri ◽  
Rozana Liko ◽  
Jorge E. Hernández Hernández
Keyword(s):  
Integral Inequalities ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Special Cases ◽  
Preinvex Functions

In this work the authors establish a new generalized version of Montgomery’s identity in the setting of quantum calculus. From this result, some new estimates of Ostrowski type inequalities are given using preinvex functions. Given the generality of preinvex functions, particular q —integral inequalities are established with appropriate choice of the parametric bifunction. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, a briefly conclusion is given.

scholarly journals Some Trapezium-Like Inequalities Involving Functions Having Strongly n-Polynomial Preinvexity Property of Higher Order

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Fractional Calculus ◽  
Higher Order ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions ◽  
Class Of Functions

The main objective of this paper is to introduce a new class of preinvex functions which is called as n-polynomial preinvex functions of a higher order. As applications of this class of functions, we discuss several new variants of trapezium-like inequalities. In order to obtain the main results of the paper, we use the concepts and techniques of k-fractional calculus. We also discuss some special cases of the obtained results which show that the main results of the paper are quite unifying one.

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.

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