• Sonuç bulunamadı

Lemma 4.2 de elde etmi¸s oldu¼gumuz (99) özde¸sli¼gine benzer olarak yeni özde¸slikler elde edilerek ilk olarak tan¬mlam¬¸s oldu¼gumuz Teorem 4.2 deki (95)e¸sitsizli¼gi olan kesirli integralleri çin Hermite-Hadamard tipli yeni e¸sit- sizlikler elde edilebilir.

KAYNAKLAR

A.G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28 (1994), 7-12.

Agrawal, Om P., Formulation of Euler-Lagrange Equations for Frac- tional Variational Problems, J. Math. Anal. Appl, 272, 368-379, (2002).

Babakhani, A., Daftardar-Gejji, V., On Calculus of Local Fractional Derivatives, J. Math. Anal. Appl., 270, 66-79, (2002).

Bertram, R., Fractional Calculus and Its Applications, Springer-Verlag, Berlin Heidelberg , (1975).

Butzer, P.L., Westphal, U., An Introduction to Fractional Calculus, in: R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scienti…c, New Jersey, (2000).

E. Set, M. E. Özdemir, and S. S. Dragomir, On the Hermite-Hadamard inequality and other integral inequalities involving two functions, Journal of Inequalities and Applications, Article ID 148102, 9 pages, (2010).

E. Set, M. E. Özdemir, and S. S. Dragomir, On Hadamard-Type in- equalities involving several kinds of convexity, Journal of Inequalities and Applications, Article ID 286845, 12 pages, (2010).

Podlubny, I., Fractional Di¤erential Equations, Academic Press, Lon- don, (1999).

Oldham, K.B., Spainer, J., The Fractional Calculus, Academic Press, New York and London, (1974).

Miller, K.S., Ross, B., An Introduction to the Fractional Calculus and Fractional Di¤erential Equations, John Wiley & Sons, New York, (1974).

Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives – Theory and Applications, Gordon and Breach, Longhorne, PA, (1993).

Özen, S., Kesirsel Türevler ·Için Opial E¸sitsizlikleri, Yüksek Lisans Tezi, Erciyes Üniversitesi, Kayseri, (2003).

Özen, S.,Öztürk, ·I., Grünwald-Letnikov,Riemann-Liouville ve Caputo kesirsel türevleri üzerine, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Der- gisi, 20(1-2),66-76 Kayseri, (2004).

M. Alomari and M. Darus, On the Hadamard’s inequality for log-convex functions on the coordinates, Journal of Inequalities and Applications, vol. 2009, Article ID 283147, 13 pages, (2009).

G. Anastassiou, M.R. Hooshmandasl, A. Ghasemi and F. Moftakharzadeh, Montogomery identities for fractional integrals and related fractional in- equalities, J. Ineq. Pure and Appl. Math., 10(4) (2009), Art. 97.

M.K. Bakula, M.E. Özdemir, J. Peµcari´c, Hadamard tpye inequalities for m convex and ( ; m)-convex functions, J. Ineq. Pure and Appl. Math., 9(4) (2008), Art. 96.

M. K. Bakula and J. Peµcari´c, Note on some Hadamard-type inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 74, (2004).

S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) (2009), Art. 86.

Z. Dahmani, New inequalities in fractional integrals, International Jour- nal of Nonlinear Scinece, 9(4) (2010), 493-497.

Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.

Z. Dahmani, L. Tabharit, S. Taf, Some fractional integral inequalities, Nonl. Sci. Lett. A, 1(2) (2010), 155-160.

Z. Dahmani, L. Tabharit, S. Taf, New generalizations of Gruss inequality usin Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3) (2010), 93-99.

S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, (2000).

S. S. Dragomir and R.P. Agarwal, Two inequalities for di¤erentiable mappings and applications to special means of real numbers and to trape- zoidal formula, Appl. Math. lett., 11(5) (1998), 91-95.

S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m convex functions, Tamkang J. Math., 3(1) (2002).

P. M. Gill, C. E. M. Pearce, and J. Peµcari´c, Hadamard’s inequality for r- convex functions, Journal of Mathematical Analysis and Applications, vol. 215, no. 2, pp. 461–470, (1997).

R. Goren‡o, F. Mainardi, Fractional calculus: integral and di¤erential equations of fractional order, Springer Verlag, Wien (1997), 223-276.

U.S.K¬rmac¬,M.K.Bakula,M.E.Özdemir,J.Peµcari´c, Hadamard-tpye inequal- ities for s-convex functions, Appl. Math. and Comp., 193 (2007), 26-35.

S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Di¤erential Equations, John Wiley & Sons, USA, (1993), p.2.

M. E. Özdemir, M. Avci, and E. Set, On some inequalities of Hermite- Hadamard type via m-convexity, Applied Mathematics Letters, vol. 23, no. 9, pp. 1065–1070, (2010).

J.E. Peµcari´c, F. Proschan and Y.L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.

I. Podlubni, Fractional Di¤erential Equations, Academic Press, San Diego, (1999).

M.Z. Sarikaya and H. Ogunmez, On new inequalities via Riemann- Liouville fractional integration, arXiv:1005.1167v1, submitted.

EKLER

1. Dördüncü bölümde ele al¬nan Kesirli integraller için Hermite-Hadmard tipi e¸sitsizlikler "M athematical and Computer M odelling(SCI)" dergisinde yay¬nlanm¬¸st¬r.

Kesirli integraller için a¸sa¼g¬daki çal¬¸smalar yap¬larak yay¬na gönderilmi¸stir. 2. M. Z. SARIKAYA and H YALDIZ, New generalization fractional of Ostrowski-Gruss type.

3. M. Z. SARIKAYA and H. YALDIZ, On weighted Montgomery identi- ties for Riemann-Liouville fractional integrals.

4. M. Z. SARIKAYA, H. YALDIZ and N. BA¸SAK, New fractional in-

equalities of Ostrowski-Gruss type.

5. M. Z. SARIKAYA, H. YALDIZ and E. SET, On fractional inequalities via Montgomery identities integrals.

ÖZGEÇMİŞ

Kişisel Bilgiler

Soyadı, Adı : YALDIZ, Hatice Uyruğu : T.C

Doğum tarihi ve Yeri : 02.04.1987 / OSMANİYE Telefon : (0546) 578 78 00

e-mail : yaldizhatice@gmail.com Eğitim

Derece Eğitim Birimi Mezuniyet Tarihi

Yüksek Lisans Düzce Ü. /Matematik B. 2012 Lisans A.Kocatepe Ü. /Matematik B. 2010 Lise Atatürk Lisesi 2003

İş Deneyimi

Yıl Yer Görev

2010-2011 Karacan Akademi Matematik Öğrt.

Yabancı Dil

İngilizce

Yayınlar

1. Mehmet Zeki SARIKAYA, Erhan SET, Hatice YALDIZ and Nagihan BAŞAK , Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities.

2. Mehmet Zeki SARIKAYA and Hatice YALDIZ, New generalization fractional of Ostrowski-Gruss type.

3. Mehmet Zeki SARIKAYA and Hatice YALDIZ , On Hermite- Hadamard type inequalities for strongly log-convex functions.

4. Mehmet Zeki SARIKAYA, Hatice YALDIZ and Hakan BOZKURT, On the Hadamard type integral inequalities involving several log-convex functions.

5. Mehmet Zeki SARIKAYA and Hatice YALDIZ, On weighted Montgomery identities for Riemann-Liouville fractional integrals.

6. Mehmet Zeki SARIKAYA, Hatice YALDIZ and Nagihan BAŞAK, New fractional inequalities of Ostrowski-Gruss type.

7. Mehmet Zeki SARIKAYA, Hatice YALDIZ and Hakan BOZKURT, On the Hadamard type integral inequalities involving several -r- convex functions.

8. Mehmet Zeki SARIKAYA and Hatice YALDIZ, On the Hadamard’s type inequalities for L-Lipschitzian mapping.

9. Mehmet Zeki SARIKAYA, Hatice YALDIZ and Erhan SET, On fractional inequalities via Montgomery identities integrals.

Benzer Belgeler