# zbMATH — the first resource for mathematics

Fixed point of contractive mappings in generalized metric spaces. (English) Zbl 1240.54119
The authors prove the existence of a fixed point for a contractive mapping of Boyd and Wong type acting on a generalized metric space.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54E40 Special maps on metric spaces
##### Keywords:
generalized metric space; contractive mapping; fixed point
Full Text:
##### References:
 [1] BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37. · Zbl 0963.54031 [2] BOYD, D. W.– WONG, J. S. W.: On nonlinear contraction, Proc. Amer. Math. Soc. 20 (1969), 458–464. · Zbl 0175.44903 [3] ĆIRIĆ, LJ. B.: A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267–273. · Zbl 0291.54056 [4] DAS, P.: A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sci. 9 (2002), 29–33. [5] EDELSTEIN, M.: On fixed and periodic points under contraction mappings, J. London Math. Soc. (2) 37 (1962), 74–79. · Zbl 0113.16503 [6] LAHIRI, B. K.– DAS, P.: Fixed point of a Ljubomir Ćirić’s quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen 61 (2002), 589–594. · Zbl 1006.54059 [7] RAKOTCH, E.: A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), 459–465. · Zbl 0105.35202 [8] REICH, S.– ZASLAVSKI, A. J.: Almost all non-expansive mappings are contractive, C.R. Math. Acad. Sci. Soc. R. Can. 22 (2000), 118–124. · Zbl 0971.47039 [9] REICH, S.– ZASLAVSKI, A. J.: The set of non contractive mappings is {$$\sigma$$}-porous in the space of all non-expansive mappings, C. R. Math. Acad. Sci. Paris 333 (2001), 539–544. · Zbl 1001.47036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.