{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:36:09Z","timestamp":1760060169708,"version":"build-2065373602"},"reference-count":8,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad Nacional Santiago Ant\u00fanez de Mayolo"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article presents a method for proving several theorems that enable the determination of the maxima and minima of certain classes of real-valued functions with vector variables, without relying on the classical theory based on partial derivatives. However, the main objective of this work is not to compare this approach with existing methods but, rather, to extend the study of extrema in real functions of vector variables that are not differentiable, as illustrated in Example 1. Each theorem is accompanied by various examples that demonstrate its applicability. The results are based on Theorems 1 and 2, as well as the selection of an appropriate connection between Theorem 2 and the functions to be optimized. Additionally, definitions related to the hierarchy between variables within a given domain are introduced, providing the theoretical framework necessary for the development of the proposed results.<\/jats:p>","DOI":"10.3390\/axioms14080611","type":"journal-article","created":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T10:13:51Z","timestamp":1754475231000},"page":"611","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Results on Maxima and Minima of Real Functions of Vector Variables: A New Perspective"],"prefix":"10.3390","volume":"14","author":[{"given":"Bibiano Martin","family":"Cerna Magui\u00f1a","sequence":"first","affiliation":[{"name":"Academic Department of Mathematics, Science Faculty, Santiago Ant\u00fanez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5360-8189","authenticated-orcid":false,"given":"Dik Dani","family":"Lujerio Garcia","sequence":"additional","affiliation":[{"name":"Academic Department of Mathematics, Science Faculty, Santiago Ant\u00fanez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8788-9775","authenticated-orcid":false,"given":"Victor","family":"Pocoy Yauri","sequence":"additional","affiliation":[{"name":"Academic Department of Mathematics, Science Faculty, Santiago Ant\u00fanez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9164-9267","authenticated-orcid":false,"given":"Vladimir Giovanni","family":"Rodriguez Sabino","sequence":"additional","affiliation":[{"name":"Academic Department of Mathematics, Science Faculty, Santiago Ant\u00fanez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru"}]},{"given":"Ruben Mario","family":"Leiva Bernuy","sequence":"additional","affiliation":[{"name":"Academic Department of Mathematics, Science Faculty, Santiago Ant\u00fanez de Mayolo National University, Shancayan Campus, Av. Centenario 200, Huaraz 02000, Peru"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"984","DOI":"10.13189\/ms.2021.090614","article-title":"Some Results on Number Theory and Differential Equations","volume":"9","year":"2021","journal-title":"Math. Stat."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"012011","DOI":"10.1088\/1742-6596\/1558\/1\/012011","article-title":"Some results on natural numbers represented by quadratic polynomials in two variables","volume":"1558","author":"Maguina","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_3","first-page":"845","article-title":"Some results on prime numbers","volume":"118","author":"Maguina","year":"2018","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"931","DOI":"10.13189\/ms.2021.090609","article-title":"Some Results on Integer Solutions of Quadratic Polynomials in Two Variables","volume":"9","author":"Ramos","year":"2021","journal-title":"Math. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"661","DOI":"10.13189\/ms.2023.110407","article-title":"Some Results on Sequences in Banach Spaces","volume":"11","author":"Maguina","year":"2023","journal-title":"Math. Stat."},{"key":"ref_6","unstructured":"Groetsch, C.W. (1980). Elements of Applicable Functional Analysis, 2nd Printing ed., Marcel Dekker."},{"key":"ref_7","unstructured":"Demidovich, B.P. (1980). Problemas y Ejercicios de An\u00e1lisis Matem\u00e1tico, Ediciones Paraninfo."},{"key":"ref_8","unstructured":"Spiegel, M.R. (2004). C\u00e1lculo Superior, McGraw-Hill."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/611\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:24:21Z","timestamp":1760034261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,6]]},"references-count":8,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["axioms14080611"],"URL":"https:\/\/doi.org\/10.3390\/axioms14080611","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,8,6]]}}}