On the extended Kimʼs p-adic q-deformed fermionic integrals in the p-adic integer ring

The purpose of this paper is to derive some applications of umbral calculus by using extended fermionic p-adic q  -integral on ZpZp. From those applications, we derive some new interesting properties on the new family of Euler numbers and polynomials. That is, a systemic study of the class of Sheffer sequences in connection with generating function of the weighted q-Euler polynomials is given in the present paper.