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

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

The Endogeneity of the Natural Rate of Growth: An Application to Turkey

The purpose of this paper is to examine the sensitivity of the Turkish economy’s natural rate of growth to the actual rate of growth, covering the period 1980-2008. To determine the reason why the natural rate of growth is endogenous, the long-run and the causality relationships between real gross domestic product and each of the production factors (labour force and physical capital stock) are investigated with the bounds test. The natural rate of growth for the Turkish economy is found to be at 4.97 percent and it increases approximately 35.6 percent in the boom periods; indicating endogeneity. However, according to the causality test results, the endogeneity of the natural rate of growth may be attributed to the total factor productivity rather than the labour force and physical capital stock. This result is important and the debate on this subject may lead to further studies.The natural rate of growth, The endogeneity of the natural rate of growth, ARDL approach, Causality tests

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

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