Periodic and fixed point theorems in a quasi-metric space. (English) Zbl 0765.54040

Ćirić, Ljubomir B.

J. Aust. Math. Soc., Ser. A 54, No. 1, 80-85 (1993).

Summary: General periodic and fixed point theorems are proved for a class of selfmaps of a quasi-metric space which satisfy a certain contractive definition (A). Two examples are presented to show that the class of mappings which satisfy (A) is indeed wider than a class of selfmaps which satisfy Caristi’s contractive definition. A common fixed point theorem for a pair of maps is established.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
47H10	Fixed-point theorems

Keywords:

complete quasi-metric space; periodic and fixed point theorems; Caristi’s contractive definition