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Now showing items 1-10 of 51

#### A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbers

(SPRINGEROPEN, 2015-01-31)

The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials (or ...

#### Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p-Laplacian operator

(SPRINGER INTERNATIONAL PUBLISHING AG, 2015-02-11)

In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: D-q(gamma)(phi(p)(D(q)(delta)y(t))) + f(t,y(t)) = 0 ...

#### On the von Staudt-Clausen's theorem related to q-Frobenius-Euler numbers

(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016-02)

In this paper, we introduce q-Frobenius-Euler numbers and derive some new properties. From those properties, we show that this number is a p-adic integer, and can be expressed by von Staudt-Clausen's theorem. We also get ...

#### On weighted q-Daehee polynomials with their applications

(Elsevier B.V., 2019-03)

In this paper, we first consider a generalization of Kim's p-adic q-integral on Z p including parameters α and β. By using this integral, we introduce the q-Daehee polynomials and numbers with weight α,β. Then, we obtain ...

#### Applications of fourier series and zeta functions to Genocchi polynomials

(Natural Sciences Publishing, 2018-09-01)

In this paper, we firstly consider the properties of Genocchi polynomials, Fourier series and Zeta functions. In the special cases, we see that the Fourier series yield Zeta functions. From here, we show that zeta functions ...

#### Multifarious implicit summation formulae of Hermite-based poly-Daehee polynomials

(Natural Sciences Publishing USA, 2018-03-01)

In this paper, we introduce the generating function of Hermite-based poly-Daehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermite-based ...

#### A Class of Generating Functions for a New Generalization of Eulerian Polynomials with their Interpolation Functions

(UNIV NIS, 2016)

Motivated by a number of recent investigations, we define and investigate the various properties of a new family of the Eulerian polynomials. We derive useful results involving these Eulerian polynomials including (for ...

#### Some (p, q)-analogues of Apostol type numbers and polynomials

(UNIV TARTU PRESS, 2019-06)

We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several ...

#### Generating functions of binary products of k-Fibonacci and orthogonal polynomials

(SPRINGER-VERLAG ITALIA SRL, 2019-07)

In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Pell numbers and Tchebychev polynomials of first and second kind. By making use of the new operator defined ...

#### FULLY DEGENERATE HERMITE POLY-BERNOULLI NUMBERS AND POLYNOMIALS

(MILI PUBL, 2018-04)

In the paper, we first introduce the fully degenerate Hermite poly-Bernoulli polynomials and investigate their properties. Next we derive the implicit summation formulae and general symmetry identities by making use of ...