Some fixed point theorems. (English) Zbl 0772.54041

Subrahmanyam, P. V.; Reilly, I. L.

J. Aust. Math. Soc., Ser. A 53, No. 3, 304-312 (1992).

Author’s summary: “Banach’s contraction principle guarantees the existence of a unique fixed point for any contractive self-mapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach’s theorem carry over to spaces whose topologies are generated by families of quasi- pseudometrics”.

Reviewer: S.L.Singh (Rishikesh)

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
47H10	Fixed-point theorems
54E40	Special maps on metric spaces

Keywords:

sequentially complete; quasi-gauge space; Banach’s contraction principle; completeness of the space; contractiveness of the mapping; spaces whose topologies are generated by families of quasi-pseudometrics