数学与计算机科学 |
|
|
|
|
分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式 |
孙文兵 |
邵阳学院 理学与信息科学系, 湖南 邵阳 422000 |
|
New Hermite-Hadamard-type inequalities for s-convex functions via fractional integrals |
SUN Wenbing |
Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan Province, China |
[1] SET E, ÖZDEMIR M E, DRAGOMIR S S. On the Hermite-Hadamard inequality and other integral inequalities involving two functions[J]. J Inequal Appl,2010:Article ID 148102. [2] LATIF M A. Inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are convex with applications[J]. Arab J Math Sci,2015,21(1):84-97. [3] ALOMARI M W, DARUS M, KIRMACI U S. Some inequalities of Hermite-Hadamard type for s-convex functions[J]. Acta Mathematica Scientia,2011,31(4):1643-1652. [4] BAKULA M K, ÖZDEMIR M E, PEARIC' J. Hadamard-type inequalities for m-convex and (α,m)-convex functions[J]. J Inequal Pure and Appl Math,2007,9(4):Article 96. [5] LATIF M A, SHOAIB M. Hermite-Hadamard type integral inequalities for differentiable m-preinvex and (α,m)-preinvex functions[J]. Journal of the Egyptian Mathematical Society,2015,23:236-241. [6] ÖZDEMIR M E, AVCI M, KAVURMACI H. Hermite-Hadamardtype inequalities via (α,m)-convexity[J]. Comput Math Appl,2011,61:2614-2620. [7] ÖZDEMIR M E, YILDIZ Ç, AKDEMIR A O, et al. On some inequalities for s-convex functions and applications[J]. Journal of Inequalities and Applications,2013,2013:333. [8] SARIKAYA M Z, SET E, YALDIZ H, et al. Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities[J]. Math Comput Model,2013,57:2403-2407. [9] SET E. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals[J]. Comput Math Appl,2012,63:1147-1154. [10] WANG J R, ZHU C C, ZHOU Y. New generalized Hermite-Hadamard type inequalities and applications to special means[J]. Journal of Inequalities and Applications,2013,2013:325. [11] ÖZDEMIR M E, DRAGOMIR S S, YILDIZ Ç. The Hadamard inequalities for convex function via fractional integrals[J]. Acta Mathematica Scientia,2013,33(5):1293-1299. [12] KIRMACI U S. Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula[J]. Appl Math Comput,2004,147:137-146. [13] KIRMACI U S, ÖZDEMIR M E. On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula[J]. Appl Math Comput,2004,153:361-368. [14] HUDZIK H, MALIGRANDA L. Some remarks on s-convex functions[J]. Aequationes Math,1994,48:100-111. [15] DRAGOMIR S, FITZPATRICK S. The Hadamard's inequality for s-convex functions in the second sense[J]. Demonstratio Math,1998,31(3):633-642. [16] GRADSHTEYN I S, RYZHIK I M. Tables of Integrals, Series, and Products[M]. San Diego:Academic Press,2000. [17] ÖZÇAG E, EGE, GÜRÇAY H. An extension of the incomplete beta function for negative integers[J]. J Math Anal Appl,2008,338:984-992. [18] ÖZÇAG E, EGE, GÜRÇAY H, et,al. On partial derivatives of the incomplete beta function[J]. Applied Mathematics Letters,2008,21:675-681. |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|