Integral inequalities for some convex functions via generalized fractional integrals

被引：0
作者：
Naila Mehreen
Matloob Anwar
机构：
[1] National University of Sciences and Technology,School of Natural Sciences
来源：
Journal of Inequalities and Applications | / 2018卷
关键词：
Hermite–Hadamard inequalities; Riemann–Liouville fractional integral; Hadamard fractional integral; Katugampola fractional integral; Convex functions; -convex functions; -convex functions; 26A51; 26A33; 26D10; 26D07; 26D15;
D O I：
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摘要：
In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional integral and Hadamard fractional integral. We show that through the Katugampola fractional integral we can find a Hermite–Hadamard inequality via the Riemann–Liouville fractional integral.
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[1]  
Chen F.(2015)Extension of the Hermite–Hadamard inequality for harmonically convex functions via fractional integrals Appl. Math. Comput. 268 121-128
[2]  
Dragomir S.S.(2011)Hermite–Hadamard’s type inequality for operator convex functions Appl. Math. Comput. 218 766-772
[3]  
Dragomir S.S.(1993)Some inequalities for Stud. Univ. Babeş–Bolyai, Math. 38 21-28
[4]  
Toader G.H.(1893)-convex functions J. Math. Pures Appl. 58 171-215
[5]  
Hadamard J.(1994)Etude sur les proprietes des fonctions entieres et en particulier d’une fonction consideree par Riemann Aequ. Math. 48 100-111
[6]  
Hudzik H.(2014)Some remarks on s-convex functions Hacet. J. Math. Stat. 43 935-942
[7]  
Maligranda L.(2014)Hermite–Hadamard type inequalities for harmonically convex functions Appl. Math. Comput. 237 237-244
[8]  
Iscan I.(2016)Hermite–Hadamard type inequalities for harmonically convex functions via fractional integrals Turk. J. Math. 40 1221-1230
[9]  
Iscan I.(2014)On Hermite–Hadamard type inequalities via generalized fractional integrals Bull. Math. Anal. Appl. 6 1-15
[10]  
Wu S.(2015)New approach to generalized fractional derivatives J. Egypt. Math. Soc. 23 236-241
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