{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:33:48Z","timestamp":1760146428142,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,2]],"date-time":"2024-11-02T00:00:00Z","timestamp":1730505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004233","name":"Universitat Polit\u00e8cnica de Val\u00e8ncia","doi-asserted-by":"publisher","award":["PAID-01-21","PID2022-138342NB-I00","101059609 (Re-Livestock)"],"award-info":[{"award-number":["PAID-01-21","PID2022-138342NB-I00","101059609 (Re-Livestock)"]}],"id":[{"id":"10.13039\/501100004233","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PAID-01-21","PID2022-138342NB-I00","101059609 (Re-Livestock)"],"award-info":[{"award-number":["PAID-01-21","PID2022-138342NB-I00","101059609 (Re-Livestock)"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Union\u2019s Horizon Europe","award":["PAID-01-21","PID2022-138342NB-I00","101059609 (Re-Livestock)"],"award-info":[{"award-number":["PAID-01-21","PID2022-138342NB-I00","101059609 (Re-Livestock)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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\u2013Eells 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.<\/jats:p>","DOI":"10.3390\/axioms13110760","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T10:57:20Z","timestamp":1730717840000},"page":"760","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Eccentric p-Summing Lipschitz Operators and Integral Inequalities on Metric Spaces and Graphs"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2544-8875","authenticated-orcid":false,"given":"Roger","family":"Arnau","sequence":"first","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8854-3154","authenticated-orcid":false,"given":"Enrique A.","family":"S\u00e1nchez P\u00e9rez","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5310-2559","authenticated-orcid":false,"given":"Sergi","family":"Sanjuan","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino de Vera s\/n, 46022 Valencia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Deza, M.M., and Deza, E. 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