Browsing by Author "Eker, Mustafa"

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    Master Thesis
    Zaman skalasında diamond-alfa tipi eşitsizlikler
    (2016) Eker, Mustafa; Çelik, Ömer Faruk; Yantır, Ahmet
    Inequalities are very practical part of mathematics. They give us an idea about the size of the quantities and provide an accurate estimate. In many areas of applied mathematics they also provide us a knowledge about the location of the things. One of the most practical part of the inequalities that it is usually far easier to satisfy assumptions involving inequalities that it is for those involving equations. When derivatives and inequalities are combined, we refer to them as 'differential inequalities' and they are vey useful in the analysis of solutions to nonlinear differential equations. In this thesis, diamond–α Opial dynamic inequalities are considered. Also Diamond-α forms of the Hölder, Cauchy-Schwarz inequalities which are impottant inequalities of mathematical analysis, Diamond-α Hardy type inequalities and Diamond-α Jensen inequality are stated and proved. Finally several generalizations on Diamond-α Opial Inequalities are presented.