Post kuantum analiz

This thesis consists of seventeen chapters. The first chapter is the introduction part which explains the emergence of the theory of post quantum calculus and its historical development. The second chapter includes some definitions, formulas and results belonging to quantum calculus. Some definitions, notations, formulas and results of the (p,q)-calculus including (p,q)-hypergeometric functions, (p,q)-power basis, (p,q)-Taylor formulas, (p,q)-binomial coefficients, (p,q)-exponential functions, (p,q)-antiderivative, (p,q)-integral, the fundamental theorem of (p,q)-calculus, the (p,q)-Gamma functions and the (p,q)-Beta functions are discussed in the third chapter to twelfth chapter. Also, some relations between (p,q)-derivative and divided differences are analyzed. The thirteenth chapter deals with p-adic analysis with some definitions, theorems and applications. Basic information belonging to p-adic analysis, Volkenborn integral and its properties, and fermionic integral and its properties are examined under three main heading. New generalizations of the Bernoulli, Euler and Genocchi numbers and polynomials based on (p,q)-numbers are given in the fourteenth chapter to sixteenth chapter. Then, some properties of aforementioned polynomials are investigated extensively. Also, an extension of the Haar distribution based on (p,q)-numbers is described in order to construct (p,q)-Volkenborn integral which derives Carlitz's-type (p,q)-Bernoulli polynomials and numbers. At the final chapter of this thesis, the conclusions and finding gained in this thesis are presented.