Erzincan University Journal of Science and Technology 2149-4584 Erzincan Binali Yıldırım Üniversitesi 10.18185/erzifbed.638456 Engineering Mühendislik Kesirli İntegrasyon Yardımıyla (h-s)-2-Preinveks Fonksiyonlar İçin Hermite-Hadamard Tipli Eşitsizlikler Hermite-Hadamard Type Inequalities For (𝒉−𝒔)𝟐−𝑷𝒓𝒆𝒊𝒏𝒗𝒆𝒙 Mapping Via Fractional Integrals https://orcid.org/0000-0002-6625-8464 Yağız Emetullah https://orcid.org/0000-0002-0034-778X Kavurmacı Önalan Havva 02 28 2020 13 ÖZEL SAYI I 132 144 10 25 2019 02 21 2020 Copyright © 2008, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 2008 Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi

Bu çalışmada (h-s)-2-preinveks fonksiyon sınıfı tanımlanmıştır.Bu sınıf kullanılarak Hermite-Hadamard tipli eşitsizlikler kesirli integrasyon yardımıyla elde edilmiştir. Elde edilen sonuçların literatürle desteklendiği gösterilmiştir.

In this paper, we define the (ℎ−𝑠)2−𝑝𝑟𝑒𝑖𝑛𝑣𝑒𝑥 function class. Using the (ℎ−𝑠)2−𝑝𝑟𝑒𝑖𝑛𝑣𝑒𝑥 function we will obtain new Hermite-Hadamard type inequalities with the help of fractional integrals.

 eşitsizlikler kesirli integraller Hermite-Hadamard (h-s)-2 preinveks fonksiyon sınıfı ℎ−𝑠)2−𝑝𝑟𝑒𝑖𝑛𝑣𝑒𝑥 function class inequalities fractional integrals Hermite-Hadamard inequality. Referans1:Breckner, W.W.(1978). “Stetigkeitsaussagenf üreine klas ever all gemeinerter konvexer funktionen in topologisc henlinearen räumen”. Publ. Inst. Math. (Beograd), 23: 13-20. Referans2:Das, S.,(2011). “Functional Fractional Calculus”, Springer, ISBN 978-3-642-20545-3. Referans3:Jue-You, L.(2010). “On Hadamard-typ inequalities for s-preinveks functions”, Journal of Chongqing Normal University (Natural Science) 27, 4: 5-8. Referans4:Matloka, M. (2013). “On some Hadamard-type inequalities for(h_1,h_2 )-preinvex functions on the co-ordinates”, Journal of Inequalities and Applications, 2013:227. Referans5:Matloka, M. (2015). “Hermite-Hadamard type inequalities for h-preinvex mappings via fractional integrals”, Control and Cybernetics, vol. 44, No. 2. Referans6:Mohan, S.R. Neogy, S.K. (1995), “On invex sets and preinvex functions”, J. Math. Anal. Appl., 189, p.901-908. Referans7:Noor, M.A. (2009). “Hadamard integral inequalities for product of two preinvex function”, Nonl. Anal. Forum, 14, 167-173. Referans8:Noor, M.A. Noor, K.I. Awan, M.U. Li, J. (2014). “On Hermite-Hadamard Inequalities for h-preinvex functions”, Filomat, 8(7), 1463-1474. Referans9:Özdemir, M.E. Tunç, M. Akdemir, A.O. (2013). “On (h,s)-Convex Functions and Hadamard-type Inequalities”, Int. J. Open Problems Compt. Math., Vol. 6, No. 2. Referans10:Pečarić, J. Proschan, F. And Tong, Y.L. (1992). “Convex Functions, Partial Orderings and Statistical Applications”. Academic Press, Inc., Boston, 469 pp. Referans11:Sarıkaya, M.Z. Sağlam, A. and Yıldırım, H. (2008). “On some Hadamard-type inequalities for h-convex functions”. Journal of Mathematical Inequalities, 2(3), 335-341. Referans12:Sarıkaya, M.Z. Set, E. Yaldız, H. and Başak, N. (2013). “Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities”, Math. And Comput. Modell., 57, 2403-2407. Referans13:Varošanec, S. (2007). “On h-convexity”,J. Math., Anal. Appl., Volume 326, Issue 1, 303-311. Referans14:Weir, T. andMond, B. (1988). “Preinvex functions in multiple objective optimization”, J. Math. Anal.Appl., 136, pp. 29–38.