Sevilay Kirci Serenbay

Coefficient bounds for certain subclasses of starlike functions of complex order

Abstract In this work, we determine the coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler-type differential equation of order m . Several corollaries and consequences of the main results are also considered.

Approximation by Chlodowsky type Jakimovski-Leviatan operators

We introduce a generalization of the Jakimovski-Leviatan operators constructed by A. Jakimovski and D. Leviatan (1969) in [1] and the theorems on convergence and the degree of convergence are established. We also give a Voronovskaya-type theorem. Furthermore, we study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity introduced by A.D. Gadjiev and A. Aral (2007) in [9].

On Convergence of Singular Integral Operators with Radial Kernels

In this paper, we prove the pointwise convergence of the operator \( L(f{;}x,y{;}\lambda )\) to the function \(f(x_{0},y_{0})\), as \((x,y{;}\lambda )\) tends to \( (x_{0},y_{0}{;}\lambda _{0})\) by the three parameter family of singular integral operators in \(L_{1}(Q_{1})\), where \(Q_{1}\) is a closed, semi-closed, or open rectangular region \( \times \). Here, the kernel function is radial and we take the point\( \left( x_{0},y_{0}\right) \) as a \(\mu \)-generalized Lebesgue point of \(f\).

The generalized Baskakov type operators

The use of Baskakov type operators is difficult for numerical calculation because these operators include infinite series. Do the operators expressed as a finite sum provide the approximation properties? Furthermore, are they appropriate for numerical calculation? In this paper, in connection with these questions, we define a new family of linear positive operators including finite sum by using the Baskakov type operators. We also give some numerical results in order to compare Baskakov type operators with this new defined operator.

Approximation properties for generalized Baskakov-type operators

In this paper, we give a generalization of the Baskakov-type operators introduced by Baskakov (Doklady Akademii Nauk SSSR 113:249–251, 1957 (in Russian)) and obtain some direct and inverse results for these new operators.MSC41A35, 41A36