scholarly journals Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications

2022 ◽  
Vol 7 (4) ◽  
pp. 5728-5751
Author(s):  
Muhammad Uzair Awan ◽  
◽  
Sadia Talib ◽  
Artion Kashuri ◽  
Ibrahim Slimane ◽  
...  
Keyword(s):  
Integral Inequalities ◽  
Absolute Value ◽  
Special Cases ◽  
Type Integral ◽  
Differentiable Mappings

<abstract><p>The main objective of this paper is to derive some new post quantum analogues of Dragomir–Agarwal and Iyengar type integral inequalities essentially by using the strongly $ \varphi $-preinvexity and strongly quasi $ \varphi $-preinvexity properties of the mappings, respectively. We also discuss several new special cases which show that the results obtained are quite unifying. In order to illustrate the efficiency of our main results, some applications regarding $ ({\mathrm{p}}, {\mathrm{q}}) $-differentiable mappings that are in absolute value bounded are given.</p></abstract>

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 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 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.

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 On improvements of Opial-type inequalities

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhao Changjian ◽  
Wing Sum Cheung
Keyword(s):  
Integral Inequalities ◽  
Special Cases ◽  
Type Integral

AbstractIn the present paper, we establish some new Opial-type integral inequalities in two variables. The results in special cases yield some of the interrelated results on Godunova–Levin's and Mitrinović–Pečarić's inequalities. These results provide new estimates on inequalities of this type.

scholarly journals New integral inequalities for strongly nonconvex functions involving Raina function

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2437-2456
Author(s):  
Artion Kashuri ◽  
Marcela Mihai ◽  
Muhammad Awan ◽  
Muhammad Noor ◽  
Khalida Noor
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Nonconvex Functions ◽  
Nonconvex Function ◽  
Special Cases ◽  
Type Integral ◽  
Generalized Fractional Integral ◽  
General Class Of Functions ◽  
Class Of Functions

In this paper, the authors defined a new general class of functions, the so-called strongly (h1,h2)-nonconvex function involving F??,?(?) (Raina function). Utilizing this, some Hermite-Hadamard type integral inequalities via generalized fractional integral operator are obtained. Some new results as a special cases are given as well.

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."

On generalization of weighted Ostrowski type inequalities for functions of bounded variation

2018 ◽  
Vol 11 (04) ◽  
pp. 1850049 ◽  
Author(s):  
Huseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Functions Of Bounded Variation ◽  
Special Cases ◽  
Type Integral

In this paper, some generalization of weighted Ostrowski type integral inequalities for mappings of bounded variation are obtained and some interesting inequalities as special cases are given.

scholarly journals On the Hermite-Hadamard-Mercer Type Inequalities for generalized Proportional Fractional Integrals

2020 ◽  
Author(s):  
Seda KILINÇ YILDIRIM ◽  
Hüseyin Yıldırım
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Absolute Value ◽  
Proportional Integral ◽  
Type Integral

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di&curren;er- antiable mappings whose derivatives in absolute value are convex.

Sign in / Sign up

Export Citation Format

Share Document