Ege M.E.Alaca C.2024-07-222024-07-22201520081898http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/16207The purpose of this paper is to define new concepts, such as T-orbitally w-completeness, orbitally w- continuity and almost weakly w-contractive mapping in the modular metric spaces. We prove some fixed point theorems for these related concepts and mappings in this space. Further, we give an application using the technique in [Lj. B. Ćirić, B. Samet, H. Aydi, C. Vetro, Appl. Math. Comput., 218 (2011), 2398-2406] and show that our results can be applied to homotopy. © 2015 All rights reserved.EnglishAll Open Access; Gold Open AccessArticle10.22436/jnsa.008.06.01