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Some stability results are obtained and the coincidence point problem involving two multi-valued operators is also studied. The best proximity point problem in vector-valued metric spaces is finally discussed.<\/jats:p>","DOI":"10.1007\/s10957-025-02758-6","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T06:42:30Z","timestamp":1751006550000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Existence and stability theorems in vector-valued metric spaces for fixed point and coincidence point problems governed by multi-valued weak contractions"],"prefix":"10.1007","volume":"206","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5629-5667","authenticated-orcid":false,"given":"Adrian","family":"Petru\u015fel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriela","family":"Petru\u015fel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,27]]},"reference":[{"key":"2758_CR1","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1017\/S0004972700033116","volume":"59","author":"QH Ansari","year":"1999","unstructured":"Ansari, Q.H., Yao, J.-C.: A fixed point theorem and its applications to a system of variational inequalities. 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