scholarly journals Improvement in companion of Ostrowski type inequalities for mappings whose first derivatives are of bounded variation and applications

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5305-5314 ◽  
Author(s):  
Hüseyin Budaka ◽  
Mehmet Sarikaya ◽  
Ather Qayyum
Keyword(s):  
Bounded Variation ◽  
Integral Inequalities ◽  
Quadrature Formulae ◽  
Special Cases ◽  
Type Integral

The main aim of this paper is to obtain a improved and generalized version of companion of Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation. Some previous results are also recaptured as special cases. New quadrature formulae are also provided.

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 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.

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 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 A new Ostrowski type inequality for functions whose first derivatives are of bounded variation

2016 ◽  
Vol 2 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Bounded Variation ◽  
Quadrature Formula ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Ostrowski Type Inequality ◽  
Type Integral

Abstract In this paper, we establish some new Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation and quadrature formula is provided

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."

scholarly journals Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings

2018 ◽  
Vol 49 (4) ◽  
pp. 317-337 ◽  
Author(s):  
Artion Kashuri ◽  
Rozana Liko ◽  
Silvestru Sever Dragomir
Keyword(s):  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Auxiliary Result ◽  
Convex Mappings ◽  
New Class ◽  
Special Cases ◽  
Type Integral

In this article, we first introduced a new class of generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings and two interesting lemmas regarding Gauss-Jacobi and\\ Hermite-Hadamard type integral inequalities. By using the notion of generalized\\ $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convexity and the first lemma as an auxiliary result, some new estimates 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 Caputo $k$-fractional derivatives are obtained. It is pointed out that some new special cases can be deduced from main results of the article.

scholarly journals On Opial’s Type Integral Inequalities

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 375
Author(s):  
Chang-Jian Zhao
Keyword(s):  
Higher Order ◽  
Integral Inequalities ◽  
Partial Derivatives ◽  
Special Cases ◽  
Type Integral ◽  
New Inequalities

In the article we establish some new Opial’s type inequalities involving higher order partial derivatives. These new inequalities, in special cases, yield Agarwal-Pang’s, Pachpatte’s and Das’s type inequalities.

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