Shivam BajpeyiSardar Vallabhbhai National Institute of Technology Surat | SVNIT · Department Of Applied Mathematics & Humanities
Shivam Bajpeyi
Doctor of Philosophy
Currently working on sampling and reconstruction of signals in different function spaces !!
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18
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Introduction
Publications
Publications (18)
This paper introduces a novel family of Kantorovich-type deep neural network operators based on Riemann–Liouville fractional integrals. Building upon the work of Costarelli (Math Model Anal 27(4):547–560, 2022) and Sharma and Singh (J Math Anal Appl 533(2):128009, 2024), we investigate the approximation properties of these operators in the spaces \...
In this paper, we aim to provide a general paradigm for dealing with the sampling and random sampling problem in a reproducing kernel subspace of Orlicz space [Formula: see text]. We consider the function space [Formula: see text] as the image of an idempotent integral operator on [Formula: see text], where the integral kernel satisfies certain off...
In this paper, we address the random sampling problem for the
class of functions in the space of Mellin band-limited functions
B_{T} , which are concentrated on a bounded cube. It is established that any Mellin band-limited function can be approximated by an element in a finite-dimensional subspace of B_{T} . Utilizing the notion of covering number...
In this paper, we address the random sampling problem for the class of Mellin band-limited functions BT which is concentrated on a bounded cube. It is established that any function in BT can be approximated by an element in a finite-dimensional subspace of BT. Utilizing the notion of covering number and Bernstein's inequality to the sum of independ...
In this paper, we introduce and analyze the approximation properties of bivariate generalization for the family of Kantorovich-type exponential sampling series. We derive the basic convergence result and Voronovskaya-type theorem for the proposed sampling series. Using the logarithmic modulus of smoothness, we establish the quantitative estimate of...
In the present article, we derive certain direct approximation
results for the family of exponential sampling-type neural network operators. The Voronovskaja type theorem of convergence for these operators is
proved. Further, the Jackson-type inequalities concerning the order of approximation for this family of operators are established by utilizin...
In the present article, an inverse approximation result and saturation order for the Kantorovich exponential sampling series $I_{w}^{\chi}$ are established. First we obtain a relation between the generalized exponential sampling series $S_{w}^{\chi}$ and $I_{w}^{\chi}$ for the space of all uniformly continuous and bounded functions on $\mathbb{R}^{...
In the present article, we derive some approximation results concerning the order of convergence for a family of Durrmeyer type exponential sampling operators. Further, we improve the rate of approximation by constructing linear combinations of these operators. At the end, we provide a few examples of the kernel functions to which the presented the...
In the present article, we introduce and analyse the approximation properties of the new family of exponential sampling type neural network operators activated by the sigmoidal functions. We derive the pointwise and uniform convergence theorem and study the order of approximation for these family of operators. Further, we establish the quantitative...
In the present article, we extend our study of Kantorovich type exponential sampling operators introduced in [4]. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional. Further, we improve the order of approximation by using the convex type linear combinations of these ope...
In the present article, we extend the theory of exponential sampling type neural network operators to the max-product setting. The approximation properties of these operators activated by the sigmoidal functions have been studied by using the moment type approach. We establish the point-wise and uniform approximation theorem for these operators alo...
In this article, we analyze the approximation properties of the new family of Durrmeyer type exponential sampling operators. We derive the point-wise and uniform approximation theorem and Voronovskaya type theorem for these generalized family of operators. Further, we construct a convex type linear combination of these operators and establish the b...
We analyse the approximation properties of the bivariate generalization of the family of Kantorovich type exponential sampling series. We derive the point-wise and Voronovskaya type theorem for these sampling type series. Using the modulus of smoothness, we obtain the quantitative estimate of order of convergence of these series. Further, we establ...
In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series (Iwχ)w>0.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usep...
In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for \( f \in C^{(2)}({\mathbb {R}}^{2})\) (the space of all continuous functions with upto second order partial derivatives are continuous and bounded on \( {\mathbb {R}}^{2}).\) Further, we introduce the generalized Boolean sum (GBS) operators of bivariate Ka...
In this article, we analyse the Kantorovich type exponential sampling operators and its linear combination. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional. Further, we improve the order of approximation by using the convex type linear combinations of these operators...
In this article, we analyze the behaviour of the new family of Kantorovich type exponential sampling series. We obtain the point-wise approxi mation theorem and Voronovskaya type theorem for the series. Further, we obtain a representation formula and an inverse result approximation for these operators. Finally, we give some examples of kernel funct...
