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A common fixed point theorem of Meir and Keeler type. (English) Zbl 0790.54054

The authors introduce the concept of compatible mappings of type (A) on a metric space, which is equivalent to the concept of compatible mappings under some conditions, and give a common fixed point theorem of Meir and Keeler type. The results presented in this paper generalize and improve some results of A. Meir and E. Keeler [J. Math. Anal. Appl. 28, 326-329 (1969; Zbl 0194.449)], S. Park and J. S. Bae [Ark. Mat. 19, 223-228 (1981; Zbl 0483.47040)], R. P. Pant [Indian J. Pure Appl. Math. 17, 187-192 (1986; Zbl 0581.54031)] and I. H. N. Rao and K. P. R. Rao [ibid. 16, 1249-1262 (1985; Zbl 0594.54031)].

MSC:

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