Hadamard and Fejér–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals

被引:0
作者
Abbas G. [1 ,2 ]
Farid G. [3 ]
机构
[1] Department of Mathematics, Government College Bhalwal, Sargodha
[2] Department of Mathematics, University of Sargodha, Sargodha
[3] Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Attock
关键词
Fractional integral operators; Hadamard inequality; Harmonically convex function;
D O I
10.1007/s41478-017-0032-y
中图分类号
学科分类号
摘要
In this paper we are interested to present the Hadamard and the Fejér–Hadamard type integral inequalities for harmonically convex functions via two sided generalized fractional integral operator. Presented results have connection with some known results about the Hadamard and the Fejér–Hadamard type inequalities for two sided Riemann–Liouville fractional integral operator. © 2017, Forum D'Analystes, Chennai.
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页码:107 / 119
页数:12
相关论文
共 17 条
[1]  
Hermite-Hadamard type inequalities for harmonically convex functions, Journal of Applied Mathematics 2014:Article ID386206, (2014)
[2]  
Dalir M., Bashour M., Applications of fractional calculus, Applied Mathematical Sciences, 4, 21, pp. 1021-1032, (2010)
[3]  
Farid G., Hadamard and Fejér-Hadamard Inequalities for generalized fractional integrals involving special functions, Konuralp Journal of Mathematics, 4, 1, pp. 108-113, (2016)
[4]  
Farid G., Pecaric J., Tomovski Z., Opial-type inequalities for fractional integral operator involving Mittag-Leffler function, Fractional Differential Calculus, 5, 1, pp. 93-106, (2015)
[5]  
Iscan I., Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, 43, 6, pp. 935-942, (2014)
[6]  
Iscan I., Wu S., Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Applied Mathematics and Computation, 238, pp. 237-244, (2014)
[7]  
Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, (2006)
[8]  
Kunt M., Iscan I., Yazi N., Gozutok U., On new inequalities of Hermite Hadamard Fejér type inequalities for harmonically convex functions via fractional integrals, SpringerPlus, 5, pp. 1-19, (2016)
[9]  
Laurent H., Sur le calcul des derivees a indicies quelconques, Nouvelles Annales de Mathematiques, 3, 3, pp. 240-252, (1884)
[10]  
Letnikov A.V., Theory of differentiation with an arbitray index (Russian), Matematicheskii Sbornik, 3, pp. 1-66, (1868)