{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:02:14Z","timestamp":1775088134231,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If \u03bb denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to obtain a uniform approximation of a continuous vector-valued function by these operators when \u03bb\u2265m+1. By using three-dimensional parametric plots, we illustrate this uniform approximation for some vector-valued functions. Finally, the influence in approximation by regular summability processes is studied, and their motivation is shown.<\/jats:p>","DOI":"10.3390\/axioms12121124","type":"journal-article","created":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T06:53:16Z","timestamp":1702623196000},"page":"1124","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Vector-Valued Shepard Processes: Approximation with Summability"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7779-6877","authenticated-orcid":false,"given":"Oktay","family":"Duman","sequence":"first","affiliation":[{"name":"Department of Mathematics, TOBB Economics and Technology University, S\u00f6\u011f\u00fct\u00f6z\u00fc, 06560 Ankara, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8990-2320","authenticated-orcid":false,"given":"Biancamaria Della","family":"Vecchia","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma \u2018Sapienza\u2019, 00185 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shepard, D. 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