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On The Convex Functions With Some Integral Inequalities

Show simple item record Mahmoud Yousef Al Agha 21/10/2020 21/10/2020 2020-10-21T10:17:55Z 21/10/2020 2020-10-21T10:17:55Z 2/20/2017
dc.description.abstract ABSTRACT In this thesis we introduce some main results from the theory of convex functions and Jensen's and related Inequalities. Also we present a detailed study of an important type of inequalities called Steffensen's Inequality. The aim of the this thesis is to provide a systematic study of some but important integral inequalities with a focus on Steffensen's type, which find numerous applications in special functions, special means and other fields in mathematics. Steffensen's inequality deals with the comparison between integrals over a whole interval and integrals over a subinterval of . Many mathematicians presented scientific papers in this field, for example, Mercer, Pecaric, Hayashi, Wu, Srivastava and Cerone. We study some generalizations belong to these scientists, and we give good contributions as applications for special functions, special means and integral mean and we also study new generalizations of Steffensen's inequality. We focus on the concept of convex sets, and convex and concave functions. Also we offer some basic inequalities associated with convex functions. We study Jensen and Jensen-Steffensen inequalities, and offer some generalization of Steffensen's inequality. We focus on the work of Pecaric and Wu-Srivastava and give some new generalizations. Also we offer some new extensions for Cerone's generalizations which were obtained by using the ideas of Pecaric. en_US
dc.language.iso en_US en_US
dc.title On The Convex Functions With Some Integral Inequalities en_US
dc.type Thesis en_US

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