Sadettin Kursun

This paper is devoted to construction of multidimensional Kantorovich modifications of exponential sampling series, which allows to approximate suitable measurable functions by considering their mean values on just one section of the function involved. Approximation behavior of newly con- structed operators is investigated at continuity points for...

In this paper, we generalize the family of exponential sampling series for functions of n variables and study their pointwise and uniform convergence as well as the rate of convergence for the functions belonging to space of log-uniformly continuous functions. Furthermore, we state and prove the generalized Mellin-Taylor’s expansion of multivariate...

In this paper, we introduce Mellin-Steklov exponential samplingoperators of order $r,r\in\mathbb{N}$, by considering appropriate Mellin-Steklov integrals. We investigate the approximation properties of these operators in continuousbounded spaces and $L^p, 1 \leq p < \infty$ spaces on $\mathbb{R}_+.$ By using the suitablemodulus of smoothness, it is...

In the present paper, we analyze the behavior of the exponential‐type generalized sampling Kantorovich operators Kωφ,G$$ {K}_{\omega}^{\varphi, \mathcal{G}} $$ when discontinuous signals are considered. We present a proposition for the series Kωφ,G$$ {K}_{\omega}^{\varphi, \mathcal{G}} $$, and we prove using this proposition certain approximation t...

In this paper, we investigate the approximation properties of exponential sampling series within logarithmically weighted spaces of continuous functions. Initially, we demonstrate the pointwise and uniform convergence of exponential sampling series in weighted spaces and present the rates of convergence via a suitable modulus of continuity in logar...

In this paper, we introduce a family generalized Kantorovich-type exponential sampling operators of bivariate functions by using the bivariate Mellin-Gauss-Weierstrass operator. Approximation behaviour of the series is established at continuity points of log-uniformly continuous functions. A rate of convergence of the family of operators is present...

The present paper deals with construction of a new family of exponential sampling Kantorovich operators based on a suitable fractional-type integral operators. We study convergence properties of newly constructed operators and give a quantitative form of the rate of convergence thanks to logarithmic modulus of continuity. To obtain an asymptotic fo...

In this paper, we introduce a new family of operators by generalizing Kantorovich type of exponential sampling series by replacing integral means over exponentially spaced intervals with its more general analogue, Mellin Gauss Weierstrass singular integrals. Pointwise convergence of the family of operators is presented and a quantitative form of th...