Erdoğan Şen

Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the boundary condition

Abstract In this work, a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition and with transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.

Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem

In this work, a discontinuous boundary-value problem with retarded argument that contains a spectral parameter in the transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. Copyright

On the von Staudt-Clausen's theorem associated with q-Genocchi numbers

Recently, the von Staudt-Clausens theorem for q-Euler numbers was introduced by Kim (2013) andq-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt-Clausens theorem for q-Genocchi numbers and also get the Kummer-type congruence for q-Genocchi numbers.

The Legendre Polynomials Associated with Bernoulli, Euler, Hermite and Bernstein Polynomials

In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.

On calculation of eigenvalues and eigenfunctions of a Sturm-Liouville type problem with retarded argument which contains a spectral parameter in the boundary condition

In this study, a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition and with transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.MSC (2010): 34L20; 35R10.

Some New Formulae for Genocchi Numbers and Polynomials Involving Bernoulli and Euler Polynomials

We give some new formulae for product of two Genocchi polynomials including Euler polynomials and Bernoulli polynomials. Moreover, we derive some applications for Genocchi polynomials to study a matrix formulation.

On a Sturm–Liouville type problem with retarded argument

In this work, a Sturm–Liouville-type problem with retarded argument, which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. Copyright

On a Discontinuous Sturm—Liouville Type Problem with Retarded Argument

In this work a discontinuous boundary‐value problem with retarded argument which contains spectral parameters in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.

q-Bernstein-Type Polynomials for Functions of Two Variables with Their Generating and Interpolation Functions

The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second kind Stirling numbers and generalized Bernoulli polynomials. Moreover, we give the generating function and interpolation function of these modified q-Bernstein polynomials of two variables and also give the derivatives of these polynomials and their generating function.

Existence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations with -Laplacian Operator and Identities on the Some Special Polynomials

We consider the following boundary-value problem of nonlinear fractional differential equation with -Laplacian operator , , , , , where , are real numbers, are the standard Caputo fractional derivatives, , , , , , are parameters, and are continuous. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence results for positive solutions, in terms of the parameters and are obtained. The uniqueness of positive solution on the parameters and is also studied. In the final section of this paper, we derive not only new but also interesting identities related special polynomials by which Caputo fractional derivative.