Jensen inequality for B-convex functions and its applications

Jensen Inequality is giving a sufficient and necessary condition for convex functions. Both this important inequality is using to determine to convexity of a function and it is practical tool to obtain some considerable inequalities. In this work, after giving information of literature and required information about the subject, the Jensen Inequality is expressed. When handing the inequality for some classic convex functions and variables, obtaining besides mean inequalities as arithmetic-geometric inequalities, Minkowski Inequality and Holder Inequality, which are important and has difficult proof, is shown. In this thesis, B-convexity which is an abstract convexity type. Previously, the Jensen Inequality for B-convex functions was proven; in the thesis both its generalizations and its applications and its different forms are proved, it is supported by examples.