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Common fixed point and invariant approximation theorems for mappings satisfying generalized contraction principle. (English) Zbl 1229.54064

Summary: We prove common fixed point theorems for weakly compatible mappings satisfying a generalized contraction principle by using a control function. As an application, we establish an invariant approximation result. Our theorems generalize recent results existing in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)