Some conclusions and inequalities on (P,K)-gama function

Objective: In this study; the definitions, properties, and relations between Gamma functions and k-gamma, p-gamma and (p,k)-gamma functions, which are generalizations of k, p and p,k, are examined in the light of literature and some integral inequalities including these functions are given. Material and Methods: All articles and books on the subject are the research materials. The articles given in the references section were examined as a research technique, and then the study was carried out using mathematical proof methods. Results: This thesis consists of four parts. After the introduction, in the second part, some basic definitions, theorems and features that will be used in other parts of the thesis are given. In the third chapter, the definition of the (p,k)-generalization (deformation, analog) of the gamma function is given. In addition, some properties of this function and its relations with gamma, k-gamma and p-gamma functions were examined. In the fourth chapter, some inequalities including the (p,k)-gamma function and its derivatives are given by making use of inequalities Hölder, Minkowski and Young. Conclusion: In this master's thesis; the (p,k)-gamma function, which is a generalization of the gamma function, is introduced and its properties and relations with other related expansion functions are examined in detail. In addition, inequalities and results involving the (p,k)-gamma function and its derivatives are obtained. Considering the importance of the gamma function and its applications in the literature, this thesis will shed light on future studies. In addition, it will be an instructive and guiding resource for researchers who want to have basic information about this subject.