On Some Approximation Processes Generated by Integrated Means on Noncompact Real Intervals-Reference-Cited by-同舟云学术

On Some Approximation Processes Generated by Integrated Means on Noncompact Real Intervals

Published:2023-10-14 Issue:6 Volume:78 Page:
ISSN:1422-6383
Container-title:Results in Mathematics
language:en
Short-container-title:Results Math

Author:

Altomare Francesco,Cappelletti Montano Mirella,Leonessa Vita^ORCID

Abstract

AbstractThe purpose of the present paper is to carry out a detailed study of a sequence of positive linear operators acting on continuous function spaces on an arbitrary real interval and constructed by means of (Borel) integrated means with respect to two families of probability Borel measures on the underlying interval and a positive real parameter. The study is mainly focused on their approximation properties in weighted spaces of continuous functions with respect to wide classes of weights. Pointwise estimates as well as weighted norm estimates are also established. In the final section a weighted asymptotic formula is obtained.

Funder

Università degli Studi della Basilicata

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Mathematics (miscellaneous)

Link

https://link.springer.com/content/pdf/10.1007/s00025-023-02023-0.pdf

Reference17 articles.

1. Altomare, F., Campiti, M.: Korovkin-type approximation theory and its applications. De Gruyter Studies in Mathematics, 17, Walter de Gruyter & Co., Berlin (1994)

2. Altomare, F., Cappelletti Montano, M., Leonessa, V., Raşa, I.: Markov Operators, Positive Semigroups and Approximation Processes. De Gruyter Studies in Mathematics 61, Walter de Gruyter GmbH, Berlin-Boston (2014)

3. Altomare, F., Cappelletti Montano, M., Leonessa, V.: On some representation formulae for operator semigroups in terms of integrated means. To appear in Dolomites Res. Notes Approx. (2023)

4. Altomare, F.: Korovkin-type theorems and approximation by positive linear operators. Surv. Approx. Theory 5, 92–164 (2010)

5. Altomare, F., Amiar, R.: Asymptotic formulae for positive linear operators. Dedicated to the 70th anniversary of Academician Blagovest Sendov. Math. Balkanica 16(1–4), 283–304 (2002)