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Weighted Approximation By Max-Product Generalized Exponential Sampling Series

Satyaranjan Pradhan, Madan Mohan Soren

Abstract

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.

Weighted Approximation By Max-Product Generalized Exponential Sampling Series

Abstract

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.
Paper Structure (3 sections, 10 theorems, 58 equations)

This paper contains 3 sections, 10 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results for Generalized Exponential Sampling Series

Key Result

Lemma 2.1

Let $\hbox{\large$\chi$}$ be a bounded function satisfying $(\hbox{\large$\chi$}_{1})$ with $\mu > 0$.Then $m_{\nu}(\hbox{\large$\chi$}) < \infty$ for every $0 \leq \nu \leq \mu$

Theorems & Definitions (11)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Definition 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Theorem 3.4
  • ...and 1 more