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In this paper, we give some informations about the Ostrowski type inequality and (alpha, m) -logaritmically convex functions. And then, we establish some Ostrowski type inequalities for this class of functions.

In this paper, we introduce the notion of -convex dominated function and present some properties of them. Finally, we present a version of Hermite-Hadamard-type inequalities for -convex dominated functions. Our results generalize the Hermite-Hadamard-type inequalities in Dragomir et al. (Tamsui Oxford Univ. J. Math. Sci. 18(2):161-173, 2002), KavurmacA +/- et al. (New Definitions and Theorems via Different Kinds of Convex Dominated Functions, 2012) and A-zdemir et al. (Two new different kinds of convex dominated functions and inequalities via Hermite-Hadamard type, 2012).

Bu tezde, bazı farklı türden konveks fonksiyonlar kullanılarak yeni tanımlamalar, örneklemeler yapılmış olup bu türden konveks fonksiyonlar ve literatürde bulunan bazı konveks fonksiyonlar için integral eşitsizlikleri elde edilmiştir. İlk bölüm giriş niteliğinde olup, bu bölümde konveks fonksiyonlar ve eşitsizlikler ile günümüze kadar yapılan çalışmalarla ilgili bilgiler verilmiştir. İkinci bölümde tezde kullanılan konveks fonksiyon kavramları, bunlar arasındaki hiyerarşi, temel teoremler ve pozitif reel sayıların bazı özel ortalamaları verilmiştir. Üçüncü bölümde, farklı türden konveks fonksiyonlar için literatürde bulunan Hermite-Hadamard tipli ve Ostrowski tipli integral eşitsizlikler verilmiştir. Bu bölümün son kısmında ise lemmalar ve bu lemmalara bağlı olarak elde edilen eşitsizlikler verilmiştir. Dördüncü bölümde ise farklı türden konveks fonsiyon sınıfları kullanılarak yeni baskın konveks fonksiyon kavramları tanımlanmış, bu yeni fonksiyon sınıfları için Hermite-Hadamard tipli integral eşitsizlikleri elde edilmiştir. Daha sonra sırasıyla konveks fonksiyonlar için yeni Hermite-Hadamard tipli; s-konveks ve m-konveks fonksiyonlar için yeni Ostrowski tipli integral eşitsizlikleri elde edilmiştir. Elde edilen sonuçlardan birçoğunun literatürü desteklediği gözlemlenmiştir. In this thesis, new definitions, and exemplifications are provided by using several different convex functions, and for those types of convex functions and for some convex functions in the literature, integral inequalities were obtained. The first section is the introduction section that includes information about the convex functions, inequalities, and the studies has been carried out until now. In the second section, the information related to convex function concepts which were used in the thesis, the hierarchy among them, basic theorems, and some special means of positive real numbers were provided. In the third section, Hermite-Hadamard type and Ostrowski type integral inequalities in the literature were given for different kinds of convex functions. In the last part of this section, lemmas, and inequalities acquired from those lemmas were presented. In the fourth section, new convex-dominated function concepts were defined by using different types of convex functions, and for those new classes of functions Hermite-Hadamard type, integral inequalities were obtained. Then, new Hermite-Hadamard type integral inequalities were obtained for convex functions, new Ostrowski type integral inequalities were obtained for s-convex and m-convex functions, respectively. Most of the results obtained from the research were observed supporting the literature. 115

In this paper, we establish several new inequalities for functions whose second derivative in absolute value aroused to the qth (q >= 1) power are (alpha, m)-convex. Some applications to special means of positive real numbers are also given. (C) 2011 Elsevier Ltd. All rights reserved.

In this paper, two new lemmas are proved and inequalities are established for co-ordinated convex functions and co-ordinated s-convex functions.

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

In this paper, we establish some integral inequalities for functions whose second derivatives in absolute value are (��,m)- convex., This paper is published in Computers & Mathematics with Applications (Volume 61, Issue 9, May 2011, Pages 2614-2620)

In this paper, we establish several new inequalities for functions whose second derivative in absolute value aroused to the qth(q≥1) power are (α,m)-convex. Some applications to special means of positive real numbers are also given.