Fractional Integral Inequalities for Different Functions

Yıl 2015, Cilt: 3 Sayı: 2, 110 - 117, 19.01.2015

Çetin Yildiz M. Emin Özdemir Havva Kavurmacı Önelan

https://izlik.org/JA39US62HR

Öz

In this paper, we establish several inequalities for different convex mappings that are connected with the Riemann-Liouvillefractional integrals. Our results have some relationships with certain integral inequalities in the literature

Anahtar Kelimeler

Hadamard Inequality , Riemann-Liouville Fractional Integration , Minkowski Inequality

Fractional integral inequalities for different functions

https://izlik.org/JA39US62HR

Öz

Kaynakça

• E.K. Godunova and V.I. Levin, Neravenstra dlja funccii sirokogo klassa soderzascego vypuklye, monotonnye i nekotorye drugie vidy funkaii, Vycislitel Mat. i Mt. Fiz., Mezvuzov Sb. Nauc. Trudov. MPGI, Moscow, 1985, 138-142.
• S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) (2009), Art. 86.
• M. Bombardelli and S. Varoˇsanec, Properties of h−convex functions related to the Hermite-Hadamard-Fej´er inequalities, Computers and Mathematics with Applications, 58 (2009), 1869-1877.
• P. Burai and A. H´azy, On approximately h−convex functions, Journal of Convex Analysis, 18 (2) (2011).
• Z. Dahmani, New inequalities in fractional integrals, International Journal of Nonlinear Science, 9(4) (2010), 493-497.
• Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51
• Z. Dahmani and L. Tabharit, S. Taf, Some fractional integral inequalities, Nonl. Sci. Lett. A., 1(2) (2010), 155-160.
• Z. Dahmani, L. Tabharit and S. Taf, New generalizations of Gr¨uss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3) (2010), 93-99.
• S.S. Dragomir, J. Peˇcari´c and L.E. Persson, Some inequalities of Hadamard Type, Soochow Journal of Mathematics, Vol.21, No:3, pp. 335-341, July 1995.
• P.M. Gill, C.E.M. Pearce and J. Peˇcari´c, Hadamard’s inequality for r-convex functions, Journal of Math. Analysis and Appl., 215 (1997), 461-470.
• N.P.G. Ngoc, N.V. Vinh and P.T.T. Hien, Integral inequalities of Hadamard-type for r-convex functions, International Mathematical Forum, 4 (2009), 1723-1728.
• M.E. ¨Ozdemir, H. Kavurmacı and M. Avcı, New inequalities of Ostrowski type for mappings whose derivatives are (α,m)-convex via fractional integrals, RGMIA Research Report Collection, 15(2012), Article 10, 8 pp.
• M.E. ¨Ozdemir, H. Kavurmacı and C¸ . Yıldız, Fractional integral inequalities via s-convex functions, arXiv:1201.4915v1 [math.CA] 24 Jan 2012.
• C.E.M. Pearce, J. Peˇcari´c and V. Simic, Stolarsky Means and Hadamard’s Inequality, Journal Math. Analysis Appl., 220 (1998), 99
• M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On some new inequalities of Hadamard type involving h−convex functions, Acta Math. Univ. Comenianae, Vol. LXXIX, 2 (2010), pp. 265-272.
• M. Z. Sarıkaya, A. Sa˘glam and H. Yıldırım, On some Hadamard-type inequalities for h-convex functions, Journal of Mathematical Inequalities, 2 (3) (2008), 335-341.
• M. Z. Sarıkaya, E. Set, H. Yaldiz and N. Bas¸ak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57, 9-10 (2013), 2403-2407.
• E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Comput. Math. Appl., 63, 7 (2012), 1147-1154.
• S. Varoˇsanec, On h−convexity, J. Math. Anal. Appl., 326 (2007), 303-311.
• G.S. Yang, D.Y. Hwang, Refinements of Hadamard’s inequality for r-convex functions, Indian Journal Pure Appl. Math., 32 (10), 2001, 1571-1579.