Fixed point theorems in best approximation theory. (English) Zbl 0834.54026

Jungck, G.; Sessa, S.

Math. Jap. 42, No. 2, 249-252 (1995).

Using some ideas of the paper by the first author [Proc. Am. Math. Soc. 103, No. 3, 977-983 (1988; Zbl 0661.54043)], the authors prove a new fixed point theorem. Applying this theorem they obtain a result in best approximation theory which generalizes an earlier one from the paper [S. A. Sahab, M. S. Khan and the second author, J. Approximation Theory 55, 349-351 (1988; Zbl 0676.41031)]. A similar result is given for Banach spaces satisfying the Opial condition.

Reviewer: J.Matkowski (Bielsko-Biała)

MSC:

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

Keywords:

best approximation; Opial condition

Citations:

Zbl 0661.54043; Zbl 0676.41031