{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:17:08Z","timestamp":1760149028786,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:00:00Z","timestamp":1688342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Chongqing of China","award":["cstc2020jcyj-msxmX0762","2104\/09926601","451-03-47\/2023-01\/200134"],"award-info":[{"award-number":["cstc2020jcyj-msxmX0762","2104\/09926601","451-03-47\/2023-01\/200134"]}]},{"name":"Initial Funding of Scientific Research for High-level Talents of Chongqing Three Gorges University of China","award":["cstc2020jcyj-msxmX0762","2104\/09926601","451-03-47\/2023-01\/200134"],"award-info":[{"award-number":["cstc2020jcyj-msxmX0762","2104\/09926601","451-03-47\/2023-01\/200134"]}]},{"name":"Ministry of Education, Science and Technological Development of the Republic of Serbia","award":["cstc2020jcyj-msxmX0762","2104\/09926601","451-03-47\/2023-01\/200134"],"award-info":[{"award-number":["cstc2020jcyj-msxmX0762","2104\/09926601","451-03-47\/2023-01\/200134"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The aim of this paper is to give some fixed point results in generalized Menger probabilistic metric spaces. Moreover, some nontrivial examples are presented to illustrate the superiority of the obtained results. In addition, several interesting applications are given to show that our results are meaningful and valuable.<\/jats:p>","DOI":"10.3390\/axioms12070660","type":"journal-article","created":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T01:42:47Z","timestamp":1688434967000},"page":"660","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fixed Point Results in Generalized Menger Probabilistic Metric Spaces with Applications to Decomposable Measures"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1836-2873","authenticated-orcid":false,"given":"Huaping","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404020, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3236-4410","authenticated-orcid":false,"given":"Tatjana","family":"Do\u0161enovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technology Novi Sad, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6942-4421","authenticated-orcid":false,"given":"Du\u0161an","family":"Raki\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technology Novi Sad, University of Novi Sad, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8254-6688","authenticated-orcid":false,"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,3]]},"reference":[{"key":"ref_1","first-page":"417","article-title":"On solution of a system of differential equations via fixed point theorem","volume":"27","author":"Nazam","year":"2018","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_2","first-page":"363","article-title":"Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces","volume":"38","author":"Pap","year":"2002","journal-title":"Kybernetika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9uations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/0165-0114(88)90064-4","article-title":"Fixed points in fuzzy metric spaces","volume":"27","author":"Grabiec","year":"1988","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","first-page":"107","article-title":"A fixed point theorem in Menger spaces","volume":"20","year":"1979","journal-title":"Publ. Inst. Math."},{"key":"ref_6","first-page":"5","article-title":"Contraction mappings in b-metric spaces","volume":"1","author":"Czerwik","year":"1993","journal-title":"Acta Math. Inform. Univ. Ostrav."},{"key":"ref_7","first-page":"15","article-title":"A short survey on the recent fixed point results on b-metric spaces","volume":"1","year":"2018","journal-title":"Constr. Math. Anal."},{"key":"ref_8","first-page":"40","article-title":"Some Pre\u0161i\u0107 type results in b-dislocated metric spaces","volume":"2","author":"Babu","year":"2019","journal-title":"Constr. Math. Anal."},{"key":"ref_9","first-page":"108","article-title":"Notes on some recent papers concerning F-contractions in b-metric spaces","volume":"1","author":"Kadelburg","year":"2018","journal-title":"Constr. Math. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0165-0114(96)00072-3","article-title":"Fixed point theorems for multivalued mappings in probabilistic metric spaces","volume":"88","year":"1997","journal-title":"Fuzzy Sets Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Had\u017ei\u0107, O., and Pap, E. (2001). Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-017-1560-7"},{"key":"ref_12","first-page":"5","article-title":"On the generalizations of Siegel\u2019s fixed point theorem","volume":"8","author":"Jung","year":"2001","journal-title":"Mathware Soft Comput."},{"key":"ref_13","first-page":"267","article-title":"A generalization of Banach\u2019s contraction principle","volume":"45","year":"1974","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1090\/S0002-9904-1976-14091-8","article-title":"Fixed point theorems in probabilistic analysis","volume":"82","year":"1976","journal-title":"Bull. Amer. Math. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF01706080","article-title":"Fixed points of contraction mappings on probabilistic metric spaces","volume":"6","author":"Sehgal","year":"1972","journal-title":"Math. Syst. Theory"},{"key":"ref_16","first-page":"147","article-title":"Quasi-contractive mappings in fuzzy metric spaces","volume":"12","author":"Mihet","year":"2015","journal-title":"J. Fuzzy Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.2298\/FIL1507549K","article-title":"A generalization of \u0106iri\u0107 fixed point theorems","volume":"29","author":"Kumam","year":"2015","journal-title":"Filomat"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.fss.2006.07.010","article-title":"Coincidence point theorems in probabilistic and fuzzy metric spaces","volume":"158","author":"Liu","year":"2007","journal-title":"Fuzzy Sets Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.fss.2005.05.024","article-title":"On the existence and the uniqueness of fixed points of Sehgal contractions","volume":"156","author":"Mihet","year":"2005","journal-title":"Fuzzy Sets Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Raki\u0107, D., Do\u0161enovi\u0107, T., Mitrovi\u0107, Z.D., De la Sen, M., and Radenovi\u0107, S. (2020). Some fixed point theorems of \u0106iri\u0107 type in fuzzy metric spaces. Mathematics, 8.","DOI":"10.3390\/math8020297"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1186\/s13663-015-0318-1","article-title":"An altering distance function in fuzzy metric fixed point theorems","volume":"2015","author":"Wairojjana","year":"2015","journal-title":"Fixed Point Theory Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1073\/pnas.28.12.535","article-title":"Statistical metric","volume":"28","author":"Menger","year":"1942","journal-title":"Proc. Nat. Acad. Sci. USA"},{"key":"ref_23","unstructured":"Schweizer, B., and Sklar, A. (1983). Probabilistic Metric Spaces, Elsevier."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Klement, E.P., Mesiar, R., and Pap, E. (2000). Triangular Norms, Kluwer Academic Publishers. Trends in Logic.","DOI":"10.1007\/978-94-015-9540-7"},{"key":"ref_25","first-page":"336","article-title":"Fuzzy metric and statistical metric spaces","volume":"11","author":"Kramosil","year":"1975","journal-title":"Kybernetica"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/S0165-0114(03)00179-9","article-title":"On fixed point theorems of Gregori and Sapena","volume":"144","year":"2004","journal-title":"Fuzzy Sets Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.2298\/FIL1407517D","article-title":"Fixed point theorem in fuzzy metric spaces using altering distance","volume":"28","author":"Brdar","year":"2014","journal-title":"Filomat"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/660\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:05:04Z","timestamp":1760126704000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/660"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,3]]},"references-count":27,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070660"],"URL":"https:\/\/doi.org\/10.3390\/axioms12070660","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,7,3]]}}}