scholarly journals New Parameterized Inequalities for η-Quasiconvex Functions via (p, q)-Calculus

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1523
Author(s):  
Humaira Kalsoom ◽  
Miguel Vivas-Cortez ◽  
Muhammad Idrees ◽  
Praveen Agarwal
Keyword(s):  
Comparative Literature ◽  
Quasiconvex Function ◽  
Quasiconvex Functions ◽  
Hadamard Inequality ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Left And Right ◽  
New Research ◽  
Work First

In this work, first, we consider novel parameterized identities for the left and right part of the (p,q)-analogue of Hermite–Hadamard inequality. Second, using these new parameterized identities, we give new parameterized (p,q)-trapezoid and parameterized (p,q)-midpoint type integral inequalities via η-quasiconvex function. By changing values of parameter μ∈[0,1], some new special cases from the main results are obtained and some known results are recaptured as well. Finally, at the end, an application to special means is given as well. This new research has the potential to establish new boundaries in comparative literature and some well-known implications. From an application perspective, the proposed research on the η-quasiconvex function has interesting results that illustrate the applicability and superiority of the results obtained.

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 New Estimations of Hermite–Hadamard Type Integral Inequalities for Special Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 144
Author(s):  
Hijaz Ahmad ◽  
Muhammad Tariq ◽  
Soubhagya Kumar Sahoo ◽  
Jamel Baili ◽  
Clemente Cesarano
Keyword(s):  
Special Functions ◽  
Type Inequality ◽  
Integral Inequalities ◽  
The Novel ◽  
Current Pattern ◽  
Hadamard Inequality ◽  
Special Means ◽  
Algebraic Properties ◽  
Type Integral ◽  
Generalized Integral Inequalities

In this paper, we propose some generalized integral inequalities of the Raina type depicting the Mittag–Leffler function. We introduce and explore the idea of generalized s-type convex function of Raina type. Based on this, we discuss its algebraic properties and establish the novel version of Hermite–Hadamard inequality. Furthermore, to improve our results, we explore two new equalities, and employing these we present some refinements of the Hermite–Hadamard-type inequality. A few remarkable cases are discussed, which can be seen as valuable applications. Applications of some of our presented results to special means are given as well. An endeavor is made to introduce an almost thorough rundown of references concerning the Mittag–Leffler functions and the Raina functions to make the readers acquainted with the current pattern of emerging research in various fields including Mittag–Leffler and Raina type functions. Results established in this paper can be viewed as a significant improvement of previously known results.

scholarly journals Hermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications

2021 ◽  
Vol 7 (3) ◽  
pp. 3418-3439
Author(s):  
Jamshed Nasir ◽  
◽  
Shahid Qaisar ◽  
Saad Ihsan Butt ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Operator ◽  
Real Numbers ◽  
Hadamard Inequality ◽  
Special Means ◽  
Special Cases ◽  
Derivatives Of ◽  
Quasi Convexity

<abstract><p>Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.</p></abstract>

scholarly journals Different type parameterized inequalities via generalized integral operators with applications

2021 ◽  
Vol 66 (3) ◽  
pp. 423-440
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Erentiable Function ◽  
Almost All

"The authors have proved an identity for a generalized integral operator via di erentiable function with parameters. By applying the established identity, the generalized trapezium, midpoint and Simpson 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 identi ed. Some applications of presented results to special means and new error estimates for the trapezium and midpoint quadrature formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the eld of integral inequalities."

scholarly journals New Simpson Type Integral Inequalities for s -Convex Functions and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Hamasalh ◽  
Yuming Chu
Keyword(s):  
Error Estimation ◽  
Convex Functions ◽  
Bessel Functions ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Theoretical Results

First, we consider a new Simpson’s identity. This identity investigates our main results that consist of some integral inequalities of Simpson’s type for the s –convex functions. From our main results, we obtain some special cases which are discussed in detail. Finally, some applications on the Bessel functions, special means of distinct positive real numbers, and error estimation about Simpson quadrature formula are presented to support our theoretical results.

scholarly journals Some new generalized $ \kappa $–fractional Hermite–Hadamard–Mercer type integral inequalities and their applications

2021 ◽  
Vol 7 (2) ◽  
pp. 3203-3220
Author(s):  
Miguel Vivas-Cortez ◽  
◽  
Muhammad Uzair Awan ◽  
Muhammad Zakria Javed ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Quadrature Formula ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Real Numbers ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Error Estimations ◽  
Integral Identities

<abstract><p>In this paper, we have established some new Hermite–Hadamard–Mercer type of inequalities by using $ {\kappa} $–Riemann–Liouville fractional integrals. Moreover, we have derived two new integral identities as auxiliary results. From the applied identities as auxiliary results, we have obtained some new variants of Hermite–Hadamard–Mercer type via $ {\kappa} $–Riemann–Liouville fractional integrals. Several special cases are deduced in detail and some know results are recaptured as well. In order to illustrate the efficiency of our main results, some applications regarding special means of positive real numbers and error estimations for the trapezoidal quadrature formula are provided as well.</p></abstract>

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 Some New Fractional Trapezium-Type Inequalities for Preinvex Functions

2019 ◽  
Vol 3 (1) ◽  
pp. 12 ◽  
Author(s):  
Artion Kashuri ◽  
Erhan Set ◽  
Rozana Liko
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Interesting Identity

In this paper, authors the present the discovery of an interesting identity regarding trapezium-type integral inequalities. By using the lemma as an auxiliary result, some new estimates with respect to trapezium-type integral inequalities via general fractional integrals are obtained. It is pointed out that some new special cases can be deduced from the main results. Some applications regarding special means for different real numbers are provided as well. The ideas and techniques described in this paper may stimulate further research.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

scholarly journals INVESTIGATION OF SOME RESULTS ARISING FROM POST QUANTUM CALCULUS

2020 ◽  
Vol 20 (3) ◽  
pp. 561-572
Author(s):  
GHAZALA GULSHAN ◽  
RASHIDA HUSSAIN ◽  
ASGHAR ALI
Keyword(s):  
Quantum Calculus ◽  
Special Cases ◽  
Type Integral ◽  
Integral Identities

This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and (p,q)-integrals. The purpose of this paper is to establish different type of identities for (p,q)-calculus. Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.

Sign in / Sign up

Export Citation Format

Share Document