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A common fixed point theorem using implicit relation and property (E.A) in metric spaces

Pathak H. K. (School of Studies in Mathematics, Pt.Ravishankar Shukla University, Raipur, India)
Rodriguez-López Rosana (Departamento de Analisis Matematico, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain)
Verma R.K. (Department of Mathematics, Govt. C.L.C. College Patan, Dist.-Durg, India)

In this paper, we prove a common fixed point theorem for a quadruple of mappings by using an implicit relation [6] and property (E.A) [1] under weak compatibility. Our theorem improves and generalizes the main Theorems of Popa [6] and Aamri and Moutawakil [1] .Various examples verify the importance of weak compatibility and property (E.A) in the existence of common fixed point and examples are also given to the implicit relation and to validate our main Theorem. We also show that property (E.A) and Meir-Keeler type contractive condition are independent to each other. .

Keywords: compatible mappings, implicit relation, noncompatible mappings, property (E.A), weakly compatible mappings