BibTex RIS Kaynak Göster

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

Yıl 2014, Cilt: 2 Sayı: 2, 76 - 84, 01.12.2014

Öz

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

Kaynakça

  • 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
Yıl 2014, Cilt: 2 Sayı: 2, 76 - 84, 01.12.2014

Öz

Kaynakça

  • 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
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

İmdat İşcan Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2014
Gönderilme Tarihi 4 Nisan 2015
Yayımlandığı Sayı Yıl 2014 Cilt: 2 Sayı: 2

Kaynak Göster

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. Ekim 2014;2(2):76-84.
Chicago İşcan, İmdat. “HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 2, sy. 2 (Ekim 2014): 76-84.
EndNote İşcan İ (01 Ekim 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., c. 2, sy. 2, ss. 76–84, 2014.
ISNAD İşcan, İmdat. “HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 2/2 (Ekim 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, c. 2, sy. 2, 2014, ss. 76-84.
Vancouver İşcan İ. HERMITE-HADAMARD’S INEQUALITIES FOR PREQUASIINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2014;2(2):76-84.
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