الفهرس | Only 14 pages are availabe for public view |
Abstract This thesis is devoted to 1- Discuss one of classes of the generalized convex functions in the sense of Beckenbach which are known as hyperbolic p-convex functions. 2- Study the main characterization of hyperbolic p-convex functions. 3- Extend some properties and integral inequalities (such as: Hermite- Hadamard, Andersson, Ostrowski and Trapezoid, ...) which are known for ordinary convex functions. 4- Introduce some applications for special means. The thesis consists of ve chapters: Chapter 1 This chapter is an introductory chapter. It contains denitions and basic concepts that are used throughout this thesis. It is regarded as a short survey of the basic needed material. Chapter 2 The goal of this chapter is to present a short survey of some needed denitions, basic concepts and results of two important vital topics: hyperbolic p-convex functions and supporting functions. 1 SUMMARY Chapter 3 The purpose of this chapter is to study the standard functional operations of hyperbolic p-convex functions. Furthermore, we prove that the envelope of hyperbolic p-convex functions is hyperbolic p-convex function and introduce a class BH[a; b] of functions representable as the dierence of two hyperbolic p-convex functions. The results of this chapter are accepted in Italian Journal of Pure and Applied Mathematics, vol. 43, 2018. Chapter 4 The main aim of this chapter is to derive three integral inequalities for hyperbolic p-convex functions which are closely connected with Andersson’s inequality for ordinary convex functions. The results of this chapter are published in Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, Vol. 68, 2018. presented in the 2nd National Conference for Mathematics and Applications, 2017. Chapter 5 Finally, in this chapter we prove that the higher powers of f(x) is hyperbolic p-convex function. In addition, we establish some new Hermite-Hadamard type integral inequalities for higher powers of hyperbolic p-convex functions. Also some application for special means are provided as well. The results of this chapter are under submission. |