BibTex RIS Cite

HERMITE-HADAMARD'S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Year 2014, Volume: 2 Issue: 2, 76 - 84, 01.12.2014

Abstract

In this paper, we extend some estimates of the right hand side ofHermite-Hadamard type inequality for prequasiinvex functions via fractionalintegrals

References

  • T. Antczak, Mean value in invexity analysis, Nonlinear Analysis, 60 (2005) 1471-1484.
  • M. Alomari, M. Darus and U.S. Kırmacı, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comp.and Math. with Applications, 59 (2010), 225-232.
  • M.K. Bakula, M.E. Ozdemir and J. Peˇcari´c, Hadamard type inequalities for m-convex and (α, m)-convex functions, J. Inequal. Pure Appl. Math. 9 (2008) Article 96. [Online: http://jipam.vu.edu.au].
  • A. Barani, A.G. Ghazanfari and S.S. Dragomir, Hermite-Hadamard inequality through pre- quasiinvex functions, RGMIA Res. Rep. Coll., 14 (2011), Article 48.
  • S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs,Victoria University, 2000.
  • M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80 (1981) 545-550.
  • D.A. Ion, Some estimates on the Hermite-Hadamard inequalities through quasi-convex func- tions, Annals of University of Craiova, Math. Comp. Sci. Ser., 34 (2007), 82-87.
  • I. Iscan, Hermite-Hadamard’s inequalities for preinvex functions via fractional integrals and related fractional inequalities, arXiv:1204.0272, submitted.
  • S.R.Mohan and S.K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901-908. [10] M. Aslam Noor, Some new classes of nonconvex functionss, Nonl. Funct. Anal. Appl., 11 (2006), 165-171. [11] M. Aslam Noor, On Hadamard integral inequalities invoving two log-preinvex functions, J. Inequal. Pure Appl. Math., 8 (2007), No. 3, 1-6, Article 75.
  • M. Aslam Noor, Hadamard integral inequalities for product of two preinvex function, Nonl. anal. Forum, 14 (2009), 167-173.
  • M.E. ¨Ozdemir and C¸ . Yıldız, The Hadamard’s inequality for quasi-convex functions via frac- tional integrals, RGMIA Res. Rep. Coll., 14 (2011), Article 101.
  • J. Park, Simpson-like and Hermite-Hadamard-like type integral inequalities for twice differ- entiable preinvex functions, Int. Journal of Pure and Appl. Math.,79 (4) (2012), 623-640.
  • R. Pini, Invexity and generalized Convexity, Optimization, 22 (1991) 513-525.
  • M.Z. Sarıkaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, 2012 (2012), Article ID 428983, 10 pages, doi:10.1155/2012/428983.
  • M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On some new inequalities of Hadamard type involv- ing h-convex functions, Acta Nath. Univ. Comenianae vol. LXXIX, 2 (2010), pp. 265-272.
  • M.Z. Sarıkaya, E. Set, H. Yaldız and N. Ba¸sak, Hermite-Hadamard’s inequalities for frac- tional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048.
  • E. Set, New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Computers and Math. with Appl., 63 (2012) 1147-1154. [20] T. Weir, and B. Mond, Preinvex functions in multiple objective optimization, Journal of Mathematical Analysis and Applications, 136, (1998) 29-38.
  • X.M. Yang and D. Li, On properties of preinvex functions, J. Math. Anal. Appl. 256 (2001) 229-241.
  • X.M. Yang, X.Q. Yang and K.L. Teo, Characterizations and applications of prequasiinvex functions, properties of preinvex functions, J. Optim. Theo. Appl., 110 (2001) 645-668.
  • Giresun University, Science and Art Faculty, Department of Mathematics, Giresun- TURKEY
  • E-mail address: imdat.iscan@giresun.edu.tr
Year 2014, Volume: 2 Issue: 2, 76 - 84, 01.12.2014

Abstract

References

  • T. Antczak, Mean value in invexity analysis, Nonlinear Analysis, 60 (2005) 1471-1484.
  • M. Alomari, M. Darus and U.S. Kırmacı, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comp.and Math. with Applications, 59 (2010), 225-232.
  • M.K. Bakula, M.E. Ozdemir and J. Peˇcari´c, Hadamard type inequalities for m-convex and (α, m)-convex functions, J. Inequal. Pure Appl. Math. 9 (2008) Article 96. [Online: http://jipam.vu.edu.au].
  • A. Barani, A.G. Ghazanfari and S.S. Dragomir, Hermite-Hadamard inequality through pre- quasiinvex functions, RGMIA Res. Rep. Coll., 14 (2011), Article 48.
  • S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs,Victoria University, 2000.
  • M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80 (1981) 545-550.
  • D.A. Ion, Some estimates on the Hermite-Hadamard inequalities through quasi-convex func- tions, Annals of University of Craiova, Math. Comp. Sci. Ser., 34 (2007), 82-87.
  • I. Iscan, Hermite-Hadamard’s inequalities for preinvex functions via fractional integrals and related fractional inequalities, arXiv:1204.0272, submitted.
  • S.R.Mohan and S.K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901-908. [10] M. Aslam Noor, Some new classes of nonconvex functionss, Nonl. Funct. Anal. Appl., 11 (2006), 165-171. [11] M. Aslam Noor, On Hadamard integral inequalities invoving two log-preinvex functions, J. Inequal. Pure Appl. Math., 8 (2007), No. 3, 1-6, Article 75.
  • M. Aslam Noor, Hadamard integral inequalities for product of two preinvex function, Nonl. anal. Forum, 14 (2009), 167-173.
  • M.E. ¨Ozdemir and C¸ . Yıldız, The Hadamard’s inequality for quasi-convex functions via frac- tional integrals, RGMIA Res. Rep. Coll., 14 (2011), Article 101.
  • J. Park, Simpson-like and Hermite-Hadamard-like type integral inequalities for twice differ- entiable preinvex functions, Int. Journal of Pure and Appl. Math.,79 (4) (2012), 623-640.
  • R. Pini, Invexity and generalized Convexity, Optimization, 22 (1991) 513-525.
  • M.Z. Sarıkaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstract and Applied Analysis, 2012 (2012), Article ID 428983, 10 pages, doi:10.1155/2012/428983.
  • M.Z. Sarıkaya, E. Set and M.E. ¨Ozdemir, On some new inequalities of Hadamard type involv- ing h-convex functions, Acta Nath. Univ. Comenianae vol. LXXIX, 2 (2010), pp. 265-272.
  • M.Z. Sarıkaya, E. Set, H. Yaldız and N. Ba¸sak, Hermite-Hadamard’s inequalities for frac- tional integrals and related fractional inequalities, Mathematical and Computer Modelling, DOI:10.1016/j.mcm.2011.12.048.
  • E. Set, New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Computers and Math. with Appl., 63 (2012) 1147-1154. [20] T. Weir, and B. Mond, Preinvex functions in multiple objective optimization, Journal of Mathematical Analysis and Applications, 136, (1998) 29-38.
  • X.M. Yang and D. Li, On properties of preinvex functions, J. Math. Anal. Appl. 256 (2001) 229-241.
  • X.M. Yang, X.Q. Yang and K.L. Teo, Characterizations and applications of prequasiinvex functions, properties of preinvex functions, J. Optim. Theo. Appl., 110 (2001) 645-668.
  • Giresun University, Science and Art Faculty, Department of Mathematics, Giresun- TURKEY
  • E-mail address: imdat.iscan@giresun.edu.tr
There are 21 citations in total.

Details

Journal Section Articles
Authors

İmdat İşcan This is me

Publication Date December 1, 2014
Submission Date April 4, 2015
Published in Issue Year 2014 Volume: 2 Issue: 2

Cite

APA İşcan, İ. (2014). HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 2(2), 76-84.
AMA İşcan İ. HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. October 2014;2(2):76-84.
Chicago İşcan, İmdat. “HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 2, no. 2 (October 2014): 76-84.
EndNote İşcan İ (October 1, 2014) HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 2 2 76–84.
IEEE İ. İşcan, “HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 2, no. 2, pp. 76–84, 2014.
ISNAD İşcan, İmdat. “HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 2/2 (October 2014), 76-84.
JAMA İşcan İ. HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2014;2:76–84.
MLA İşcan, İmdat. “HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 2, no. 2, 2014, pp. 76-84.
Vancouver İşcan İ. HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2014;2(2):76-84.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.