Various generalizations of metric spaces and fixed point theorems

• Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 109; no. 1; pp. 175 - 198
• Main Authors: Van An, Tran, Van Dung, Nguyen, Kadelburg, Zoran, Radenović, Stojan
• Format: Journal Article
• Language: English
• Published: Milan Springer Milan 01.03.2015; Springer Nature B.V
• Subjects: Applications of Mathematics; Equivalence; Fixed points (mathematics); Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Metric space; Original Paper; Theorems; Theoretical; Metric space; 54E99; Secondary 54D99; Generalized metric space; Primary 47H10; Fixed point; 54H25
• ISSN: 1578-7303; 1579-1505
• DOI: 10.1007/s13398-014-0173-7

There have been many attempts to generalize the definition of a metric space in order to obtain possibilities for more general fixed point results. In this paper, we give a survey of recent results on reducing fixed point theorems on generalized metric spaces to fixed point theorems on metric spaces and then investigate this fact in other generalized metric spaces. We show that many generalized metric spaces are topologically equivalent to certain metric spaces or to previously generalized metric spaces. Also, the fixed point theory in these generalized metric spaces may be a consequence of the fixed point theory in certain metric spaces or in previously generalized metric spaces.