A study involving the completion of quasi 2-normed space

The fundamental aim of this paper is to introduce and investigate a new property of quasi 2-normed space based on a question given by C. Park (2006) [2] for the completion quasi 2-normed space. Finally, we also find an answer for a question Park's.Comment: 7 page

A New Generating Function of (q-) Bernstein Type Polynomials and their Interpolation Function

The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and derivative of the (q-) Bernstein type polynomials. We also give relations between the (q-) Bernstein type polynomials, Hermite polynomials, Bernoulli polynomials of higher-order and the second kind Stirling numbers. By applying Mellin transformation to this generating function, we define interpolation of the (q-) Bernstein type polynomials. Moreover, we give some applications and questions on approximations of (q-) Bernstein type polynomials, moments of some distributions in Statistics

Analytic Continuation of weighted q-Genocchi numbers and polynomials

In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function {\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n | {\alpha}) is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted q-Genocchi polynomials.Comment: 5 pages, submitte

A note on the modified q-Dedekind sums

In the present paper, the fundamental aim is to consider a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order modified Dedekind-type sums related to q-Genocchi polynomials with weight alpha by using fermionic p-adic invariant q-integral on Zp.Comment: 6 page