T. Yurdakadim

Double sequences and Orlicz functions

In this paper we define strong A-convergence with respect to an Orlicz function for double sequences. We show, on bounded double sequences, that statistical convergence and strong A-convergence with respect to any Orlicz function are equivalent. This eliminates a condition of Demirci for bounded single (ordinary) sequences.

Approximation to Derivatives of Functions by Linear Operators Acting on Weighted Spaces by Power Series Method

In this chapter, using power series method we study some Korovkin type approximation theorems which deal with the problem of approximating a function by means of a sequence of linear operators acting on weighted spaces.

The Arzelà–Ascoli theorem by means of ideal convergence

Abstract In this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà–Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions.

SUBSEQUENTIAL RESULTS ON UNIFORM STATISTICAL CONVERGENCE

In this paper, we present some relationships between convergence and uniform statistical convergence of a given sequence and its subsequences. The results concerning uniform statistical convergence presented here are also closely related to earlier results regarding statistical convergence and almost convergence of sequences, and are dealing with measure and in a minor case with category. Finally, we present a Cauchy type characterization of uniform statistical convergence and a result concerning uniform statistical convergence of subseries of a series.

Statistical approximation properties of convolution operators for multivariables

In this paper, we study Korovkin type approximation results for a sequence of positive linear convolution operators defined on C([a,b]×[c,d]), the space of all continuous real valued functions on [a,b]×[c,d] with the use of A-statistical convergence. We also study rates of A-statistical convergence of these operators.

The Stancu-Chlodowsky operators based on q-calculus

In the present paper, we introduce a q-analogue of the Stancu-Chlodowsky operators and study rate of convergence for these operators. Actually we consider it in a more general setting via A-statistical convergence. We also obtain rate of convergence of these operators by means of modulus of continuity and Peetre-K functional.

The Buck-Pollard Property for p-Cesàro Matrices

Establishing a one-to-one correspondence between the interval (0, 1] and the collection of all subsequences of a given sequence {s n }, Buck and Pollard proved that {s n } is (C, 1)-summable if almost all of subsequences are, but not conversely. In this article, we consider the analogous questions for the p-Cesàro matrices. We show, for example, that if then a bounded sequence is C p -summable if and only if almost all of its subsequences are C p -summable.

Approximation of functions by the sequence of integral operators

Abstract In this paper, we study the approximation of the Lebesgue integrable functions at fixed characteristic points with the use of statistical convergence and matrix summability of the sequence of convolution type integral operators.