{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:31:59Z","timestamp":1760239919792,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,28]],"date-time":"2019-01-28T00:00:00Z","timestamp":1548633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main purpose in this paper is to define the modification form of random    \u03b1   -admissible and random    \u03b1   -   \u03c8   -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.<\/jats:p>","DOI":"10.3390\/sym11020143","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T03:40:55Z","timestamp":1548733255000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalized Random \u03b1-\u03c8-Contractive Mappings with Applications to Stochastic Differential Equation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4535-8984","authenticated-orcid":false,"given":"Chayut","family":"Kongban","sequence":"first","affiliation":[{"name":"KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand"},{"name":"KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5463-4581","authenticated-orcid":false,"given":"Poom","family":"Kumam","sequence":"additional","affiliation":[{"name":"KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand"},{"name":"KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3340-2781","authenticated-orcid":false,"given":"Juan","family":"Mart\u00ednez-Moreno","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Experimental Science, University of Ja\u00e9n, Campus Las Lagunillas, s\/n, 23071 Ja\u00e9n, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8496-7803","authenticated-orcid":false,"given":"Kanokwan","family":"Sitthithakerngkiet","sequence":"additional","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,28]]},"reference":[{"key":"ref_1","first-page":"462","article-title":"Zuf\u00e4llige gleichungen","volume":"5","year":"1955","journal-title":"Czechoslov. 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