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The first author was supported by a contract of the Programa de Ayudas de Investigacion y Desarrollo (PAID-01-21), Universitat Politecnica de Valencia. This research was funded by the Agencia Estatal de Investigacion grant number PID2022-138342NB-I00. The research was funded by the European Union's Horizon Europe research and innovation program under the Grant Agreement No. 101059609 (Re-Livestock).

Analysis of institutional authors

Arnau, RogerAuthorPerez, Enrique A SanchezCorresponding AuthorSanjuan, SergiAuthor

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December 8, 2024
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Eccentric p-Summing Lipschitz Operators and Integral Inequalities on Metric Spaces and Graphs

Publicated to:Axioms: Mathematical Logic And Mathematical Physics. 13 (11): 760- - 2024-11-01 13(11), DOI: 10.3390/axioms13110760

Authors: Arnau, Roger; Perez, Enrique A Sanchez; Sanjuan, Sergi

Affiliations

Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Camino Vera S-N, Valencia 46022, Spain - Author

Abstract

The extension of the concept of p-summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space M afforded by the associated Arens-Eells space, along with the duality between M and the metric dual space M# defined by the real-valued Lipschitz functions on M. However, alternative approaches to measuring distances between sequences of elements of metric spaces (essentially involved in the definition of p-summability) exist. One approach involves considering specific subsets of the unit ball of M# for computing the distances between sequences, such as the real Lipschitz functions derived from evaluating the difference in the values of the metric from two points to a fixed point. We introduce new notions of summability for Lipschitz operators involving such functions, which are characterized by integral dominations for those operators. To show the applicability of our results, in the last part of this paper, we use the theoretical tools obtained in the first part to analyze metric graphs. In particular, we show new results on the behavior of numerical indices defined on these graphs satisfying certain conditions of summability and symmetry.

Keywords

DominatioIntegral inequalitiesLipschitzMetricSummability

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Axioms: Mathematical Logic And Mathematical Physics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 66/332, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-07-16:

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

    Leadership analysis of institutional authors

    There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Arnau Notari, Andres Roger) and Last Author (Sanjuan Silvestre, Sergi).

    the author responsible for correspondence tasks has been Sánchez Pérez, Enrique Alfonso.