scholarly journals Some New Post-Quantum Integral Inequalities Involving Twice (p,q)-Differentiable ψ-Preinvex Functions and Applications

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 283
Author(s):  
Miguel Vivas-Cortez ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Muhammad Aslam Noor
Keyword(s):  
Integral Identity ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Main Motivation ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Quantum Integral ◽  
Special Means ◽  
Preinvex Functions

The main motivation of this article is derive a new post-quantum integral identity using twice (p,q)-differentiable functions. Using the identity as an auxiliary result, we will obtain some new variants of Hermite–Hadamard’s inequality essentially via the class of ψ-preinvex functions. To support our results, we offer some applications to a special means of positive real numbers and twice (p,q)-differentiable functions that are in absolute value bounded as well.

scholarly journals On post quantum estimates of upper bounds involving twice $(p,q)$-differentiable preinvex function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Integral Identity ◽  
Upper Bounds ◽  
Auxiliary Result ◽  
Differentiable Functions ◽  
Quantum Integral ◽  
Preinvex Functions

Abstract The main objective of this paper is to derive a new post quantum integral identity using twice $(p,q)$ ( p , q ) -differentiable functions. Using this identity as an auxiliary result, we obtain some new post quantum estimates of upper bounds involving twice $(p,q)$ ( p , q ) -differentiable preinvex functions.

Some new fractional integral inequalities for generalized relative semi-m-(r; h1, h2)-preinvex mappings via generalized Mittag-Leffler function

2019 ◽  
Vol 26 (1/2) ◽  
pp. 41-55 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

scholarly journals Some integral inequalities for multiplicatively geometrically P-functions

2019 ◽  
Vol 9 (2) ◽  
pp. 216-222 ◽  
Author(s):  
Huriye Kadakal
Keyword(s):  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means

In this manuscript, by using a general identity for differentiable functions we can obtain new estimates on a generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are multiplicatively geometrically P-functions. Some applications to special means of real numbers are also given.

scholarly journals Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
İmdat İşcan
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Differentiable Functions ◽  
Special Means ◽  
Harmonically Convex Functions

A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite-Hadamard and Simpson-like types for functions whose derivatives in absolute value at certain power are harmonically convex. Some applications to special means of real numbers are also given.

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.

scholarly journals Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

2021 ◽  
Vol 45 (4) ◽  
pp. 647-657
Author(s):  
İMDAT İŞCAN ◽  
◽  
TEKİN TOPLU ◽  
FATİH YETGİN ◽  
◽  
...  
Keyword(s):  
Error Estimates ◽  
Real Numbers ◽  
Absolute Value ◽  
General Identity ◽  
Differentiable Functions ◽  
Special Means ◽  
New Inequalities

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

scholarly journals Inequalities for Estimations of Integrals Related to Higher-Order Strongly n -Polynomial Preinvex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yongping Deng ◽  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Integral Identity ◽  
Higher Order ◽  
Differentiable Functions ◽  
Special Means ◽  
Preinvex Functions ◽  
New Inequalities

In this paper, we establish an integral identity associated with m -times differentiable functions. The result is then used to derive some integral estimations for higher-order strongly n -polynomial preinvex functions. Finally, we apply the obtained inequalities to construct new inequalities involving special means.

scholarly journals Some new bounds оf Gauss – Jacobi аnd Hermite – Hadamard type integral inequalities

2021 ◽  
Vol 73 (8) ◽  
pp. 1067-1084
Author(s):  
A. Kashuri ◽  
M. Ramosaçaj ◽  
R. Liko
Keyword(s):  
Error Estimates ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral

UDC 517.5 In this paper, authors discover two interesting identities regarding Gauss–Jacobi and Hermite–Hadamard type integral inequalities. By using the first lemma as an auxiliary result, some new bounds with respect to Gauss–Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite–Hadamard type integral inequalities via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from main results. Some applications to special means for different positive real numbers and new error estimates for the trapezoidal are provided as well. These results give us the generalizations, refinement and significant improvements of the new and previous known results. The ideas and techniques of this paper may stimulate further research.

scholarly journals Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable ()-Convex Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jaekeun Park
Keyword(s):  
Real Numbers ◽  
Positive Real ◽  
Absolute Value ◽  
Convex Mappings ◽  
First Derivative ◽  
Special Means

The author establish several Hermite-Hadamard and Simpson-like type inequalities for mappings whose first derivative in absolute value aroused to the th () power are ()-convex. Some applications to special means of positive real numbers are also given.

scholarly journals Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

2021 ◽  
Vol 7 (3) ◽  
pp. 3303-3320
Author(s):  
Jamshed Nasir ◽  
◽  
Shahid Qaisar ◽  
Saad Ihsan Butt ◽  
Ather Qayyum ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Integral Operator ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integral Operator ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Differentiable Functions ◽  
Second Derivatives ◽  
Preinvex Functions

<abstract><p>The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.</p></abstract>

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