الفهرس 
PreliminariesOnly 14 pages are availabe for public view
 |  | from | 135 |  |  |
| | | from | 135 | | |
Abstract
The aim of this thesis is to
1- Discuss some classes of the generalized convex functions in the sense of Beckenbach.
2- Study the main characterizations of sub E-convex functions.
3- Extend some properties and integral inequalities (such as: Hermite- Hadamard, Hermite-Hadamard-Feje´r, Ostrowski and Trapezoid, ...) which are known for ordinary convex functions.
4- Show that some results introduced by Hu¨seyin Budak [11], in (2019), are incorrect.
The thesis consists of five chapters:
Chapter 1
This chapter is an introductory chapter. It contains definitions 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 obtain some new inequalities of Hermite-Hadamard and Hermite-Hadamard-Feje´r type inequalities via fractional integrals for trigonometric ρ-convex functions. Furthermore, we use the Riemann-Liouville fractional integral to present recent re-
sults on fractional integral inequalities for trigonometric ρ-convex func- tions. Also, we show that some results introduced by Hu¨seyin Budak [11], in (2019), are incorrect. Moreover, a counter example is given to confirm our claim.
The results of this chapter are:
• under submission for publication.
Chapter 3
The purpose of this chapter is to get upper and lower estimates for product of two hyperbolic p-convex functions, which is analogous to Hermite-Hadamard type inequalities for product of two hyperbolic p-convex functions.
The results of this chapter are:
• Accepted for publication in Italian Journal of Pure and Applied Mathematics on August 3rd, 2021.
• Presented in the 3rd International Conference for Mathematics and Its Applications, 2020.
Chapter 4
The aim of this chapter is to study the standard functional op- erations of sub E-convex functions. Furthermore, we introduce a class BE[a, b] of functions representable as a difference of two sub E-convex functions.
The results of this chapter are:
Published in RGMIA Research Report Collection, Vol. 25, No. 2, 2022.
Chapter 5
Finally, in this chapter, we show that the power function of sub E-convex function f n(x) is sub E-convex function. Furthermore, we establish some new integral inequalities of Hadamard type involving sub E-convex functions and sub E-concave functions.
The results of this chapter are:
Published in Advances in Mathematics: Scientific Journal, Vol. 9, No. 3, 2020.