scholarly journals NEW HERMITE-HADAMARD TYPE INEQUALITIES VIA CONFORMABLE FRACTIONAL INTEGRALS CONCERNING DIFFERENTIABLE RELATIVE SEMI-(r; m; h1; h2)-CONVEX MAPPINGS AND THEIR APPLICATIONS

2020 ◽  
pp. 61-78
Author(s):  
Artion Kashuri
Keyword(s):  
Fractional Integrals ◽  
Convex Mappings

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 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

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

CERTAIN INTEGRAL INEQUALITIES CONSIDERING GENERALIZED m-CONVEXITY ON FRACTAL SETS AND THEIR APPLICATIONS

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950117 ◽  
Author(s):  
TINGSONG DU ◽  
HAO WANG ◽  
MUHAMMAD ADIL KHAN ◽  
YAO ZHANG
Keyword(s):  
Probability Density ◽  
Fractional Integrals ◽  
The Real ◽  
Text Type ◽  
Fractal Sets ◽  
Convex Mappings ◽  
Fractal Set ◽  
Special Means ◽  
Real Linear ◽  
Generalized Probability

First, we introduce a generalized [Formula: see text]-convexity concept defined on the real linear fractal set [Formula: see text] [Formula: see text] and discuss the relation between generalized [Formula: see text]-convexity and [Formula: see text]-convexity. Second, we present several important properties of the generalized [Formula: see text]-convex mappings. Meanwhile, via local fractional integrals, we also derive certain estimation-type results on generalizations of Hadamard-type, Fejér-type and Simpson-type inequalities. As applications related to local fractional integrals, we construct several inequalities for generalized probability density mappings and [Formula: see text]-type special means.

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.

scholarly journals Fractional integral inequalities for generalized-$$\mathbf{m }$$-$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$-convex mappings via an extended generalized Mittag–Leffler function

2019 ◽  
Vol 9 (2) ◽  
pp. 231-243
Author(s):  
George Anastassiou ◽  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Fractional Integral ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Real Numbers ◽  
Positive Real ◽  
Convex Mappings ◽  
Invex Set ◽  
Special Means ◽  
Special Cases

AbstractThe authors discover a new identity concerning differentiable mappings defined on $$\mathbf{m }$$ m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized-$$\mathbf{m }$$ m -$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$ ( ( h 1 p , h 2 q ) ; ( η 1 , η 2 ) ) -convex mappings by involving an extended generalized Mittag–Leffler function are presented. It is pointed out that some new special cases can be deduced from main results. 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.

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