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![Approximation to the function h of the family of operators Iw,α,μB3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( I_{w,\alpha ,\mu }^{B_3}\right) $$\end{document} with respect to μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}](publication/371660220/figure/fig2/AS:11431281186279264@1693878516013/Approximation-to-the-function-h-of-the-family-of-operators.png)
Approximation to the function h of the family of operators Iw,α,μB3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( I_{w,\alpha ,\mu }^{B_3}\right) $$\end{document} with respect to μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}
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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...
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Citations
... Agrawal and Baxhaku (Agrawal & Baxhaku,2025) (Butzer, 1983). This includes work on Kantorovich-type modifications (Kumar et al., 2022), (Coroianu et al., 2021) (Costarelli & Vinti, 2014), (Kursun et al., 2023), (Kursun et al., 2024a) and the exponential sampling formula (Ostrowski et al. (Ostrowsky et al., 1981), Bertero and Pike (Bertero & Pike, 1991), and Gori (Gori, 1993)), which is particularly relevant for applications involving exponentially-spaced data, such as those found in optical physics and engineering. Butzer and Jansche (Butzer & Jansche, 1998) further explored the exponential sampling formula using Mellin analysis, highlighting its suitability for handling sampling and approximation problems involving exponentially-spaced data (Butzer & Jansche, 1997). ...
... These advances have enabled the study of phenomena like light scattering and diffraction. As research continues, new applications and modifications are emerging, as seen in works covering weighted approximations by samplingtype operators (see, e.g., [1,4,6,29,35]). ...
The present paper deals with construction of newly family of Neural Network operators, that is,Steklov Neural Network operators. By using Steklov type integral, we introduce a new version of Neural Network operators and we obtain some convergence theorems for the family, such as, pointwise and uniform convergence,rate of convergence via moduli of smoothness of order r.
... For other publications on the exponential sampling series and its different forms (see, [12][13][14][15][40][41][42]). Moreover, for the approximation properties of generalized exponential sampling series and its different forms in logarithmic weighted spaces of continuous functions (see also [5][6][7]). ...
In this paper, we introduce Mellin-Steklov exponential samplingoperators of order , by considering appropriate Mellin-Steklov integrals. We investigate the approximation properties of these operators in continuousbounded spaces and spaces on By using the suitablemodulus of smoothness, it is given high order of approximation. Further, we present a quantitative Voronovskaja type theorem and we study the convergence results of newly constructed operators in logarithmic weighted spaces offunctions. Finally, the paper provides some examples of kernels that support the our results.
... Numerous results have been published on the exponential sampling series and Kantorovich forms; see, for example, [32][33][34][35][36][37][38][39][40][41][42]. For other publishes on approximation theory and sampling type series, we refer the readers to [43,44]. ...
In the present paper, we analyze the behavior of the exponential‐type generalized sampling Kantorovich operators Kωφ,G when discontinuous signals are considered. We present a proposition for the series Kωφ,G, and we prove using this proposition certain approximation theorems for discontinuous functions. Furthermore, we give several examples of kernels satisfying the assumptions of the present theory. Finally, some numerical computations are performed to verify the approximation of discontinuous functions f f by Kωφ,Gf.
... In recent years, numerous studies have been published on sampling type operators. We can refer the readers to [19,21,28,39] for generalized sampling operators, [9,11,26] for sampling Kantorovich operators, [14,24] for sampling Durrmeyer operators, [5,6,12,37] for exponential sampling type operators and [ 3,4,8,10,[34][35][36]38] for both polynomial and logarithmic weighted approximation by sampling type operators. Our aim in this paper is to construct a new form of generalized sampling operators given in (1.1) by considering a ρ function, which satisfies some suitable conditions. ...
In the present paper, we introduce a new family of sampling operators, so-called “modified sampling operators”, by taking a function ρ that satisfies the suitable conditions, and we study pointwise and uniform convergence of the family of newly introduced operators. We give the rate of convergence of the family of operators via classical modulus of continuity. We also obtain an asymptotic formula in the sense of Voronovskaja. Moreover, we investigate the approximation properties of modified sampling operators in weighted spaces of continuous functions characterized by ρ function. Finally, we present examples of some kernels that satisfy the appropriate assumptions. At the end, we present some graphical and numerical representations by comparing the modified sampling operators and the classical sampling operators.
In this article, we study the convergence behaviour of the classical generalized Max Product exponential sampling series in the weighted space of log-uniformly continuous and bounded functions. We derive basic convergence results for both the series and study the asymptotic convergence behaviour. Some quantitative approximation results have been obtained utilizing the notion of weighted logarithmic modulus of continuity.
In this research paper, we construct a new sequence of Riemann–Liouville type fractional α‐Bernstein–Kantorovich operators. We prove a Korovkin type approximation theorem and discuss the rate of convergence with the first order modulus of continuity of these operators. Further, we study Voronovskaja type theorem, quantitative Voronovskaya type theorem, Chebyshev–Grüss inequality and Grüss–Voronovskaya type theorem.
In this paper, we discuss the higher-order -Bernstein–Kantorovich operators, which are associated with the Bernstein polynomials. We analyze various aspects, such as error estimations and Voronovskaja-type asymptotic formula. Finally, we provide a comparative study by visualizing the results graphically and interpreting the upper limit of the error numerically.
