Work

A nonlinear version of Kantorovich operators with p-averages: convergence results and asymptotic formula

Year: 2026

Type: article

Abstract: In this paper, we modify the classical Kantorovich operators, very well known in Approximation Theory, by considering p -averages (whose expressions are of the form of $$L^p$$ L p (quasi-)norms, $$p>0$$ p > 0 ). We establish convergence results, an asymptotic formula covering the general setting; moreover, we show that, under suitable assumptions, our operators perform better than the classical Kantorovich ones in approximating functions. Because of the nature of the p -averages, the proposed operators are nonlinear, so their study turns out to be more challenging.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-026-01178-7

Authors: Mirella Cappelletti Montano, Rosario Corso, Vita Leonessa

Institutions: University of Bari Aldo Moro, University of Palermo, University of Basilicata

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Palermo, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni