scholarly journals Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings

2021 ◽  
Vol 6 (4) ◽  
pp. 3525-3545
Author(s):  
Yuping Yu ◽  
◽  
Hui Lei ◽  
Gou Hu ◽  
Tingsong Du ◽  
...  
Keyword(s):  
Upper Bound ◽  
Fractional Integrals ◽  
Convex Mappings ◽  
Differentiable Mappings

scholarly journals Hermite–Hadamard type inequalities via k-fractional integrals concerning differentiable generalized η-convex mappings

2020 ◽  
Vol 24 (1) ◽  
pp. 19-35
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Convex Mappings ◽  
Invex Set ◽  
Special Means ◽  
Special Cases ◽  
Differentiable Mappings

The authors discover a new identity concerning differentiable mappings dened on (m; g; θ)-invex set via k-fractional integrals. By using the obtained identity as an auxiliary result, some new estimates with respect to Hermite–Hadamard type inequalities via k-fractional integrals for generalized-m-(((h1 ∘g)p; (h2 ∘g)q); (η1; η2))-convex mappings are presented. It is pointed out that some new special cases can be deduced from the main results. Also, some applications to special means for different positive real numbers are provided.

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 Some New Hermite-Hadamard Type Inequalities Via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r;m,p,q,h1,h2)-Preinvex Mappings

2018 ◽  
Vol 60 (1) ◽  
pp. 59-78
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integrals ◽  
Auxiliary Result ◽  
Invex Set ◽  
Special Cases ◽  
Differentiable Mappings

Abstract In this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r;m,p,q,h1,h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

scholarly journals Hermite-Hadamard-Mercer type inequalities for fractional integrals

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2425-2436
Author(s):  
Hatice Öğulmüş ◽  
Zeki Sarıkay
Keyword(s):  
Present Note ◽  
Fractional Integrals ◽  
Absolute Value ◽  
The Right ◽  
Differentiable Mappings

In the present note, we proved Hermite-Hadamard-Mercer inequalities for fractional integrals and we established some new fractional inequalities connected with the right and left-sides of Hermite-Hadamard-Mercer type inequalities for differentiable mappings whose derivatives in absolute value are convex.

scholarly journals On Hermite-Hadamard Type Inequalities for s–Convex Mappings via Fractional Integrals of a Function with Respect to Another Function

2016 ◽  
Vol 57 (1) ◽  
pp. 25-36 ◽  
Author(s):  
Hüseyin Budak ◽  
Mehmet Z. Sarikaya
Keyword(s):  
Convex Function ◽  
Fractional Integrals ◽  
Convex Mappings ◽  
Hadamard Fractional Integrals

AbstractIn this paper, we obtain some Hermite-Hadamard type inequalities fors–convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.

scholarly journals Some New Hermite-Hadamard-Fejer Type Inequlaties via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r; m, h1, h2)-Preinvex Mappings

2018 ◽  
Vol 11 (1) ◽  
pp. 51
Author(s):  
Miftar Ramosacaj ◽  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integrals ◽  
Auxiliary Result ◽  
Invex Set ◽  
Special Cases ◽  
Differentiable Mappings

In this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r;m,h1,h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard-Fejer type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

scholarly journals Fractional trapezium-like inequalities involving generalized relative semi--preinvex mappings on an -invex set

2020 ◽  
Vol 72 (12) ◽  
pp. 1633-1350
Author(s):  
T. S. Du ◽  
C. Y. Luo ◽  
Z. Z. Huang ◽  
A. Kashuri
Keyword(s):  
Fractional Integral ◽  
Second Order ◽  
Fractional Integrals ◽  
Invex Set ◽  
Special Cases ◽  
Integral Equality ◽  
Differentiable Mappings

UDC 517.5 The authors derive a fractional integral equality concerning twice differentiable mappings defined on -invex set. By using this identity, the authors obtain new estimates on generalization of trapezium-like inequalities for mappings whose second order derivatives are generalized relative semi--preinvex via fractional integrals. We also discuss some new special cases which can be deduced from our main results.

scholarly journals Local fractional integrals involving generalized strongly m-convex mappings

2018 ◽  
Vol 8 (2) ◽  
pp. 95-107 ◽  
Author(s):  
George Anastassiou ◽  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integrals ◽  
Convex Mappings
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