الفهرس 
Preliminaries
Generalized convex functionsOnly 14 pages are availabe for public view
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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 de nitions
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
de nitions, 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 di erence 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.