الفهرس 
Chapter 1 Preliminary resultsOnly 14 pages are availabe for public view
 |  | from | 155 |  |  |
| | | from | 155 | | |
Abstract
The present thesis consists of six chapters and is organized as: Chapter one is an introduction to the history of the subject and a review for previous related important published studies works are given. Chapter two presents a new family of approximations of G(x). Also, some new inequalities for G(x) are deduced. In chapter three, some completely monotonic functions involving G(x) are introduced and some sharp inequalities of G(x) are presented. Next, a new proof of Slavić inequality about Wallis ratio is deduced and consequently, a new inequality for , which refines some related works is introduced. At the end, two inequalities for the hyperbolic tangent function are obtained. Chapter four presents two best approximation formulas for G(x). Also, some completely monotonic functions involving G(x) are introduced. Consequently, some new inequalities for G(x) and its derivative are obtained and they will be more accurate than some inequalities for G(x). In chapter five, completely monotonic properties related to the generalized Gamma function are presented. Consequently, some upper and lower bounds for the generalized gamma, diagamma and polygamma functions are obtained. These results generalized some results were presented by Alzer and Batir in 2007 and improved some inequalities were presented by Nantomah, Merovci and Nasiru in 2018. Chapter six presents three completely monotonic functions in terms of the generalized Gamma and digamma functions, which generalize some results were introduced by Alzer in 1997 and Qi in 2007. Also, some inequalities for the generalized gamma, diagamma and polygamma functions are obtained, which refine some recent results.