Ayşegül Erençin

Durrmeyer type modification of generalized Baskakov operators

Abstract In the present paper, Durrmeyer type modification of generalized Baskakov operators is introduced and some direct results are established for these operators.

Voronovskaya Type Theorems in Weighted Spaces

ABSTRACT In this article, we introduce a generalization of Gamma operators based on a function ρ having some properties and prove quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems via weighted modulus of continuity.

A generalization of Jain's operators

In this paper, we introduce a generalization of Jains operators based on a function ?. We examine convergence properties of such operators and prove a Voronovskaya type result.

A class of linear positive operators in weighted spaces

In this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.

Bivariate Bernstein type operators

In this paper, we introduce bivariate extension of Bernstein type operators defined in 11. We show that these operators preserve some properties of the original function f, such as Lipschitz constant and monotonicity. Furthermore, we present the monotonicity of the sequence of bivariate Bernstein type operators for n when f is ?-convex.

Some recursion relations for solutions of a class of equations

This work presents some recursion relations for solutions of a class of singular partial differential equations. The equations consist of iterated differential operators each of which involves real parameters.

Generalized Baskakov type operators

Abstract In this paper, we introduce a generalization of Baskakov operators based on a function ρ. We prove a weighted Korovkin type theorem and compute the rate of convergence via weighted modulus of continuity for these operators. Also we give a Voronovskaya type asymptotic formula.

Some preservation properties of MKZ-Stancu type operators

In this work, we construct Stancu type modification of the generalization of Meyer-Konig and Zeller operators (MKZ) defined in [12]. We show that the Lipschitz constant of a Lipschitz continuous function and the properties of the function of modulus of continuity can be retained by these operators.

Some Solutions for an Equation of Order of 4p

We obtain all solutions which depend only on r for a singular partial differential equation of order 4p. Here, the operator includes Laplacian and GASPT (Generalized Axially Symmetric Potential Theory) operator.