{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:39:45Z","timestamp":1760236785080,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,25]],"date-time":"2021-12-25T00:00:00Z","timestamp":1640390400000},"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>The aim of the paper is to introduce the Banach space consisting of real functions defined on a locally compact and countable at infinity metric space and having increments tempered by a modulus of continuity. We are going to provide a condition that is sufficient for the relative compactness in the Banach space in question. A few particular cases of that Banach space will be discussed.<\/jats:p>","DOI":"10.3390\/axioms11010011","type":"journal-article","created":{"date-parts":[[2021,12,27]],"date-time":"2021-12-27T01:00:54Z","timestamp":1640566854000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2838-5569","authenticated-orcid":false,"given":"J\u00f3zef","family":"Bana\u015b","sequence":"first","affiliation":[{"name":"Department of Nonlinear Analysis, Rzesz\u00f3w University of Technology, al. Powsta\u0144c\u00f3w Warszawy 8, 35-959 Rzeszow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4103-0746","authenticated-orcid":false,"given":"Rafa\u0142","family":"Nalepa","sequence":"additional","affiliation":[{"name":"Department of Nonlinear Analysis, Rzesz\u00f3w University of Technology, al. Powsta\u0144c\u00f3w Warszawy 8, 35-959 Rzeszow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,25]]},"reference":[{"key":"ref_1","first-page":"820437","article-title":"On the space of functions with growth tempered by a modulus of contiunuity and its applications","volume":"2013","author":"Nalepa","year":"2013","journal-title":"J. Funct. 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Fixed Point Theory Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"124237","DOI":"10.1016\/j.jmaa.2020.124237","article-title":"Solvability in H\u00f6lder spaces of an integral equation which models dynamics of the capillary rise","volume":"490","author":"Rocha","year":"2020","journal-title":"J. Math. Anal. Appl."},{"key":"ref_6","first-page":"28","article-title":"Existence results and the dimension of the solution set for a nonlocal inclusions problem with mixed fractional derivatives and integrals","volume":"2020","author":"Alsaedi","year":"2020","journal-title":"J. Nonlinear Funct. Anal."},{"key":"ref_7","first-page":"1","article-title":"Multi-term fractional q-difference equations with q-integral boundary conditions via topological degree theory","volume":"2021","author":"Boutiara","year":"2021","journal-title":"Commun. Optim. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bourbaki, N. (1989). General Topology, Springer.","DOI":"10.1007\/978-3-642-61703-4"},{"key":"ref_9","unstructured":"Sikorski, R. (1956). Real Functions I, PWN."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/1\/11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:53:20Z","timestamp":1760169200000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/1\/11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,25]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["axioms11010011"],"URL":"https:\/\/doi.org\/10.3390\/axioms11010011","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,12,25]]}}}