scholarly journals ON GENERALIZED FRACTIONAL INTEGRAL INEQUALITIES FOR FUNCTIONS OF BOUNDED VARIATION WITH TWO VARIABLES

2021 ◽  
Vol 45 (1) ◽  
pp. 49-69
Author(s):  
ARTION KASHURI ◽  
HŰSEYIN BUDAK ◽  
ROZANA LIKO ◽  
MUHAMMAD AAMIR ALI ◽  
KUBILAY ÖZÇELIK
Keyword(s):  
Bounded Variation ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Functions Of Bounded Variation ◽  
Generalized Fractional Integral

scholarly journals Sharp integral inequalities based on general Euler two-point formulae

2005 ◽  
Vol 46 (4) ◽  
pp. 555-574 ◽  
Author(s):  
J. Pečarić ◽  
I. Perić ◽  
A. Vukelić
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Functions Of Bounded Variation ◽  
Quadrature Formulae ◽  
Lipschitzian Functions ◽  
Integrable Functions

AbstractWe consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

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 Some generalized fractional integral inequalities with nonsingular function as a kernel

2021 ◽  
Vol 6 (4) ◽  
pp. 3352-3377
Author(s):  
Shahid Mubeen ◽  
◽  
Rana Safdar Ali ◽  
Iqra Nayab ◽  
Gauhar Rahman ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Generalized Fractional Integral

scholarly journals Certain generalized fractional integral inequalities

2020 ◽  
Vol 5 (2) ◽  
pp. 1588-1602 ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
◽  
Gauhar Rahman ◽  
Aftab Khan ◽  
Asifa Tassaddiq ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Generalized Fractional Integral

scholarly journals On Some Generalized Fractional Integral Inequalities for p-Convex Functions

2019 ◽  
Vol 3 (2) ◽  
pp. 29
Author(s):  
Seren Salaş ◽  
Yeter Erdaş ◽  
Tekin Toplu ◽  
Erhan Set
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Hadamard Inequality ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

In this paper, firstly we have established a new generalization of Hermite–Hadamard inequality via p-convex function and fractional integral operators which generalize the Riemann–Liouville fractional integral operators introduced by Raina, Lun and Agarwal. Secondly, we proved a new identity involving this generalized fractional integral operators. Then, by using this identity, a new generalization of Hermite–Hadamard type inequalities for fractional integral are obtained.

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 Monotonic and Nonnegative Solutions of a Nonlinear Volterra-Stieltjes Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tomasz Zając
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Bounded Variation ◽  
Fractional Integral ◽  
Functions Of Bounded Variation ◽  
Stieltjes Integral ◽  
Measures Of Noncompactness ◽  
Bounded Interval ◽  
Nonnegative Solutions ◽  
Real Functions

We study the existence of monotonic and nonnegative solutions of a nonlinear quadratic Volterra-Stieltjes integral equation in the space of real functions being continuous on a bounded interval. The main tools used in our considerations are the technique of measures of noncompactness in connection with the theory of functions of bounded variation and the theory of Riemann-Stieltjes integral. The obtained results can be easily applied to the class of fractional integral equations and Volterra-Chandrasekhar integral equations, among others.

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