tailieunhanh - báo cáo hóa học:" Research Article On the Symmetric Properties of the Multivariate p-Adic Invariant Integral on Zp Associated with the Twisted Generalized Euler Polynomials of Higher Order"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Symmetric Properties of the Multivariate p-Adic Invariant Integral on Zp Associated with the Twisted Generalized Euler Polynomials of Higher Order | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 826548 8 pages doi 2010 826548 Research Article On the Symmetric Properties of the Multivariate p-Adic Invariant Integral on Zp Associated with the Twisted Generalized Euler Polynomials of Higher Order Taekyun Kim 1 Byungje Lee 2 and Young-Hee Kim1 1 Division of General Education-Mathematics Kwangwoon University Seoul 139-701 Republic of Korea 2 Department of Wireless Communications Engineering Kwangwoon University Seoul 139-701 Republic of Korea Correspondence should be addressed to Young-Hee Kim yhkim@ Received 6 November 2009 Revised 11 March 2010 Accepted 14 March 2010 Academic Editor Ulrich Abel Copyright 2010 Taekyun Kim et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We study the symmetric properties for the multivariate p-adic invariant integral on Zp related to the twisted generalized Euler polynomials of higher order. 1. Introduction Let p be a fixed prime number. Throughout this paper the symbols Z Zp Qp and Cp denote the ring of rational integers the ring of p-adic integers the field of p-adic rational numbers and the completion of algebraic closure of Qp respectively. Let N be the set of natural numbers. The normalized valuation in Cp is denoted by p with p p 1 p. Let UD Zp be the space of uniformly differentiable function on Zp. For f e UD Zp the fermionic p-adic invariant integral on Zp is defined as r pi-1 pZ1 1 f f x dp x lim y f x p x pNlzA hm y f x -1 x M N TO N TO J Z x 0 x 0 see 1-25 . For n e N we note that f c n-1 f x n dp x -1 n f x dp x X -1 n-1-lf see 5 . JZp JZp 1 0 2 Journal of Inequalities and Applications Let d be a fixed odd positive integer. For N e N we set X Xd lim Z dpN Z X1 Zp N X u a dpZp 0 a dp a p 1 a dpNZp Ịx e X x a mod dpN Ị where a e Z lies in