Common fixed point theorems for families of weakly compatible maps. (English) Zbl 1142.54363

Ćirić, Ljubomir; Razani, A.; Radenović, Stojan; Ume, J. S.

Comput. Math. Appl. 55, No. 11, 2533-2543 (2008).

Summary: In this paper the existence and approximation of a unique common fixed point of two families of weakly compatible self-maps on a complete metric space are investigated. An example is presented to show that our results for the mappings considered satisfying non-linear contractive type conditions are genuine generalizations of the recent result for metric spaces [B. Singh and S. Jain, J. Math. Anal. Appl. 301, No. 2, 439–448 (2005; Zbl 1068.54044), Theorem 3.3] and many other known results.

MSC:

54H25

Fixed-point and coincidence theorems (topological aspects)

Keywords:

common fixed point; compatible maps; weakly compatible maps; non-linear contractive condition; Cauchy sequence

Citations:

Zbl 1068.54044

References:

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