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 New Hermite-Hadamard-Fejér inequalities via k-fractional integrals for differentiable generalized nonconvex functions

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2549-2558
Author(s):  
Artion Kashuri ◽  
Themistocles Rassias
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Nonconvex Functions ◽  
New Class ◽  
Differentiable Functions ◽  
Special Cases

The authors discover a new interesting generalized identity concerning differentiable functions via k-fractional integrals. By using the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard-Fej?r type inequalities via k-fractional integrals for a new class of function involving Raina?s function, the so-called generalized (h1, h2)-nonconvex are presented. These inequalities have some connections with known integral inequalities. Also, some new special cases are provided as well from main results.

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 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 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 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 New generalized trapezoidal type integral inequalities with applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Artion Kashuri ◽  
Ghulam Farid ◽  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Differentiable Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Numerical Computations ◽  
Special Cases ◽  
Type Integral ◽  
Almost All

AbstractTrapezoidal inequalities for functions of diverse nature are useful in numerical computations. The authors have proved an identity for a generalized integral operator via a differentiable 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 the recent decades. Various special cases have been identified. Some applications of presented results have been analyzed.

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>

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