A nonlinear version of Kantorovich operators with p-averages: convergence results and asymptotic formula
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 $$L^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> (quasi-)norms, $$p>0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). 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.
Authors
- Mirella Cappellettı Montano (ORCID: https://orcid.org/0000-0003-1850-0428)
- Rosario Corso (ORCID: https://orcid.org/0000-0001-9123-4977)
- Vita Leonessa (ORCID: https://orcid.org/0000-0001-9547-8397)
Institutions
- University of Basilicata (IT)
- University of Bari Aldo Moro (IT)
- University of Palermo (IT)
Publication Details
- Journal
- Analysis and Mathematical Physics
- Published
- 2026-04-03
- DOI
- https://doi.org/10.1007/s13324-026-01178-7
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00
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