Carlitz-type (𝓹,𝓺)-Genocchi polynomials

This thesis consists of six chapters. In the first chapter, Genocchi polynomials, 𝓆 analysis, (𝓅,𝓆) analysis and the content of the thesis were briefly mentioned. In the second chapter, basic information about 𝓆-analogue and (𝓅,𝓆)-analogue are given and then basic definitions and properties of Bernoulli, Euler, Genocchi numbers and polynomials are expressed. In the third chapter, definitions and theorems about (𝓅,𝓆)-Bernoulli, (𝓅,𝓆)-Euler and (𝓅,𝓆)-Genocchi polynomials and especially (𝓅,𝓆)-Genocchi polynomial are mentioned. In the fourth chapter, basic definitions and properties of Carlitz-type (𝓅,𝓆)-Genocchi polynomials and Carlitz-type (ℎ,𝓅,𝓆)-Genocchi polynomials are given. In the fifth chapter, based on the definitions and theorems we have obtained, the basic definitions and properties of Carlitz-type higher order (𝓅,𝓆)-Genocchi polynomials and Carlitz-type higher order (ℎ,𝓅,𝓆)-Genocchi polynomials are discussed and examined. For the order (𝓅,𝓆)-Genocchi polynomials, relations related to the symmetric property are given. In the last part of the thesis, the studies we examined were concluded.