Some New Ostrowski Type Integral Inequalities via General Fractional Integrals

2020 ◽  
pp. 135-151
Author(s):  
Artion Kashuri ◽  
Themistocles M. Rassias
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Type Integral

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 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.

NEWTON’S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALS

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050037 ◽  
Author(s):  
Sabah Iftikhar ◽  
Poom Kumam ◽  
Samet Erden
Keyword(s):  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Quadrature Rules ◽  
Special Means ◽  
Type Integral

We firstly establish an identity involving local fractional integrals. Then, with the help of this equality, some new Newton-type inequalities for functions whose the local fractional derivatives in modulus and their some powers are generalized convex are obtained. Some applications of these inequalities for Simpson’s quadrature rules and generalized special means are also given.

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."

Generalization of different type integral inequalities for generalized (𝑠, 𝑚)-preinvex Godunova–Levin functions

2018 ◽  
Vol 24 (2) ◽  
pp. 211-221
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Type Integral

Abstract In the present paper, the notion of generalized {(s,m)} -preinvex Godunova–Levin function of second kind is introduced, and some new integral inequalities involving generalized {(s,m)} -preinvex Godunova–Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite–Hadamard, Ostrowski and Simpson type inequalities for generalized {(s,m)} -preinvex Godunova–Levin functions of second kind via Riemann–Liouville fractional integral are established.

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¤er- antiable mappings whose derivatives in absolute value are convex.

scholarly journals SIMPSON’S TYPE INEQUALITIES VIA THE KATUGAMPOLA FRACTIONAL INTEGRALS FOR s-CONVEX FUNCTIONS

2021 ◽  
Vol 45 (5) ◽  
pp. 709-720
Author(s):  
SETH KERMAUSUOR ◽  
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Type Integral ◽  
Hadamard Fractional Integrals

In this paper, we introduce some Simpson’s type integral inequalities via the Katugampola fractional integrals for functions whose first derivatives at certain powers are s-convex (in the second sense). The Katugampola fractional integrals are generalizations of the Riemann–Liouville and Hadamard fractional integrals. Hence, our results generalize some results in the literature related to the Riemann–Liouville fractional integrals. Results related to the Hadamard fractional integrals could also be derived from our results.

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