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Fractional Integral Inequalities for Different Functions

Year 2015, Volume: 3 Issue: 2, 110 - 117, 19.01.2015

Abstract

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

References

  • 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.

Fractional integral inequalities for different functions

Year 2015, Volume: 3 Issue: 2, 110 - 117, 19.01.2015

Abstract

References

  • 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.
There are 20 citations in total.

Details

Journal Section Articles
Authors

Çetin Yildiz This is me

M. Emin Özdemir This is me

Havva Kavurmacı Önelan This is me

Publication Date January 19, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Yildiz, Ç., Özdemir, M. E., & Önelan, H. . K. (2015). Fractional Integral Inequalities for Different Functions. New Trends in Mathematical Sciences, 3(2), 110-117.
AMA Yildiz Ç, Özdemir ME, Önelan HK. Fractional Integral Inequalities for Different Functions. New Trends in Mathematical Sciences. January 2015;3(2):110-117.
Chicago Yildiz, Çetin, M. Emin Özdemir, and Havva Kavurmacı Önelan. “Fractional Integral Inequalities for Different Functions”. New Trends in Mathematical Sciences 3, no. 2 (January 2015): 110-17.
EndNote Yildiz Ç, Özdemir ME, Önelan HK (January 1, 2015) Fractional Integral Inequalities for Different Functions. New Trends in Mathematical Sciences 3 2 110–117.
IEEE Ç. Yildiz, M. E. Özdemir, and H. . K. Önelan, “Fractional Integral Inequalities for Different Functions”, New Trends in Mathematical Sciences, vol. 3, no. 2, pp. 110–117, 2015.
ISNAD Yildiz, Çetin et al. “Fractional Integral Inequalities for Different Functions”. New Trends in Mathematical Sciences 3/2 (January 2015), 110-117.
JAMA Yildiz Ç, Özdemir ME, Önelan HK. Fractional Integral Inequalities for Different Functions. New Trends in Mathematical Sciences. 2015;3:110–117.
MLA Yildiz, Çetin et al. “Fractional Integral Inequalities for Different Functions”. New Trends in Mathematical Sciences, vol. 3, no. 2, 2015, pp. 110-7.
Vancouver Yildiz Ç, Özdemir ME, Önelan HK. Fractional Integral Inequalities for Different Functions. New Trends in Mathematical Sciences. 2015;3(2):110-7.