scholarly journals New conformable fractional integrals of Ostrowski type using new generalized (s, m, ϕ)-preinvex mappings

2017 ◽  
Vol 3 (2) ◽  
pp. 173-185
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
Special Means

AbstractIn the present paper, the notion of new generalized (s, m, ϕ)-preinvex mapping is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving new generalized (s, m, ϕ)-preinvex mappings along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for new generalized (s, m, ϕ)-preinvex mappings via conformable fractional integrals are established. At the end, some applications to special means are given.

scholarly journals Hermite-Hadamard Type Inequalities for Mtm-Preinvex Functions

2017 ◽  
Vol 58 (1) ◽  
pp. 77-96
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
Special Means ◽  
Preinvex Functions

AbstractIn the present paper, the notion of MTm-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MTm-preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MTm-preinvex functions via classical integrals and Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These results not only extend the results appeared in the literature (see [13]), but also provide new estimates on these types.

scholarly journals Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions

2017 ◽  
Vol 3 (1) ◽  
pp. 102-115
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Beta Function ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
Type Integral ◽  
Preinvex Functions

Abstract In this paper, the notion of generalized (s; m; ξ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized (s; m; ξ)-preinvex functions along with beta function are given. Moreover, we establish some new Hermite-Hadamard type integral inequalities for products of two generalized (s; m; ξ)-preinvex functions via classical and Riemann-Liouville fractional integrals. These results not only extend the results appeared in the literature (see [10],[11]), but also provide new estimates on these types. At the end, some conclusions are given.

On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions

2019 ◽  
Vol 25 (1) ◽  
pp. 59-72
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
New Class ◽  
Special Means ◽  
Preinvex Functions

Abstract In the present paper, a new class of generalized beta {(r,g)} -preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss–Jacobi type quadrature formula involving generalized beta {(r,g)} -preinvex functions are given. Moreover, some generalizations of Hermite–Hadamard type inequalities for generalized beta {(r,g)} -preinvex functions that are twice differentiable via k-fractional integrals are established. These general inequalities give us some new estimates for Hermite–Hadamard type k-fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s,m,\varphi) -preinvex functions, Aust. J. Math. Anal. Appl. 13 2016, 1, Article ID 16]. At the end, some applications to special means are given.

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>

Hermite-Hadamard Type Fractional Integral Inequalities for Generalized (r; g; s; m; ϕ)-Preinvex Functions

2017 ◽  
Vol 59 (1) ◽  
pp. 43-55
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Quadrature Formula ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Left Hand ◽  
New Class ◽  
Preinvex Functions

AbstractIn the present paper, a new class of generalized (r; g; s; m; ϕ)-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (r; g; s; m; ϕ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized (r; g; s; m; ϕ)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see [1],[2]), but also provide new estimates on these types.

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.

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.

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