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HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS

Yıl 2016, Cilt: 4 Sayı: 1, 254 - 260, 01.04.2016

Öz

By making use of identity of the established by Sarkaya [4], some new Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral are established. Our results are the generalizations of the results obtain by Sarkaya [4].

Kaynakça

  • [1] W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), 13-20.
  • [2] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure Appl. Math. 10 (3) (2009) Art. 86.
  • [3] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 9 (4) (2010) 493{ 497.
  • [4] Z. Dahmani, On Minkowski and Hermite{Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1 (1) (2010) 51{58.
  • [5] Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonlinear. Sci. Lett. A 1 (2) (2010) 155{160.
  • [6] S.S. Dragomir J.Pecaric and L.E.Persson, Some inequalities of Hadamard type, Soochow J. Math 21 (1995), 335-241.
  • [7] H.Hudzik, L.Maligranda, Some remarks on s􀀀convex functions, Aequationes Math., 48 (1994) 100-111.
  • [8] U.S. Krmac Inequalities for di erentiable mappings and applicatons to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.
  • [9] M.Z.Sarkaya Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities II (submitted).
  • [10] M.Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann{Liouville fractional integration, Abstract and Applied Analysis, Volume 2012, Article ID 428983, 10 pages, doi:10.1155/2012/428983.
  • [11] M.Z. Sarikaya, E.Set, H.Yaldiz and N.Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities Mathematical and Computer Modelling, 57 (2013) 2403-2407.
  • [12] M.Z. Sarikaya and H. Yaldiz, On weighted Montogomery identities for Riemann-Liouville fractional integrals, Konuralp Journal of Mathematics, 1 (1) (2013) 48-53.
  • [13] E.Set, M.E.  Ozdemir, M.Z. Sarkaya, F. Karakoc, Hermite-Hadamard type inequalities for ( ;m)􀀀convex functions via fractional integrals, (submitted).
  • [14] E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Comp. Math. Appl., 63(7) (2012), 1147-1154.
  • [15] S.Varo^sanec, On h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311.
Yıl 2016, Cilt: 4 Sayı: 1, 254 - 260, 01.04.2016

Öz

Kaynakça

  • [1] W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23 (1978), 13-20.
  • [2] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure Appl. Math. 10 (3) (2009) Art. 86.
  • [3] Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 9 (4) (2010) 493{ 497.
  • [4] Z. Dahmani, On Minkowski and Hermite{Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1 (1) (2010) 51{58.
  • [5] Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonlinear. Sci. Lett. A 1 (2) (2010) 155{160.
  • [6] S.S. Dragomir J.Pecaric and L.E.Persson, Some inequalities of Hadamard type, Soochow J. Math 21 (1995), 335-241.
  • [7] H.Hudzik, L.Maligranda, Some remarks on s􀀀convex functions, Aequationes Math., 48 (1994) 100-111.
  • [8] U.S. Krmac Inequalities for di erentiable mappings and applicatons to special means of real numbers and to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.
  • [9] M.Z.Sarkaya Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities II (submitted).
  • [10] M.Z. Sarikaya, H. Ogunmez, On new inequalities via Riemann{Liouville fractional integration, Abstract and Applied Analysis, Volume 2012, Article ID 428983, 10 pages, doi:10.1155/2012/428983.
  • [11] M.Z. Sarikaya, E.Set, H.Yaldiz and N.Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities Mathematical and Computer Modelling, 57 (2013) 2403-2407.
  • [12] M.Z. Sarikaya and H. Yaldiz, On weighted Montogomery identities for Riemann-Liouville fractional integrals, Konuralp Journal of Mathematics, 1 (1) (2013) 48-53.
  • [13] E.Set, M.E.  Ozdemir, M.Z. Sarkaya, F. Karakoc, Hermite-Hadamard type inequalities for ( ;m)􀀀convex functions via fractional integrals, (submitted).
  • [14] E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals, Comp. Math. Appl., 63(7) (2012), 1147-1154.
  • [15] S.Varo^sanec, On h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Erhan Set

Mehmet Zeki Sarıkaya

Filiz Karakoç Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2016
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 1

Kaynak Göster

APA Set, E., Sarıkaya, M. Z., & Karakoç, F. (2016). HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 4(1), 254-260.
AMA Set E, Sarıkaya MZ, Karakoç F. HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. Nisan 2016;4(1):254-260.
Chicago Set, Erhan, Mehmet Zeki Sarıkaya, ve Filiz Karakoç. “HERMITE-HADAMARD TYPE INEQUALITIES FOR H-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, sy. 1 (Nisan 2016): 254-60.
EndNote Set E, Sarıkaya MZ, Karakoç F (01 Nisan 2016) HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 1 254–260.
IEEE E. Set, M. Z. Sarıkaya, ve F. Karakoç, “HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”, Konuralp J. Math., c. 4, sy. 1, ss. 254–260, 2016.
ISNAD Set, Erhan vd. “HERMITE-HADAMARD TYPE INEQUALITIES FOR H-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/1 (Nisan 2016), 254-260.
JAMA Set E, Sarıkaya MZ, Karakoç F. HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:254–260.
MLA Set, Erhan vd. “HERMITE-HADAMARD TYPE INEQUALITIES FOR H-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, c. 4, sy. 1, 2016, ss. 254-60.
Vancouver Set E, Sarıkaya MZ, Karakoç F. HERMITE-HADAMARD TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(1):254-60.
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