Abstract
A collection of fixed point theorems is generalized by replacing hypothesized commutativity or weak commutativity of functions involved by compatibility.
Highlights
The last two decades have produced a spate of articles which propose generalizations and/or extensions of the Banach Contraction Principle, which Principle states that a contraction f of a complete metric space (X,d) has a unique fixed point
Iw is a common fixed point of I, S, and T
In any case, I, S, and T have a common fixed point
Summary
The last two decades have produced a spate of articles which propose generalizations and/or extensions of the Banach Contraction Principle, which Principle states that a contraction f of a complete metric space (X,d) has a unique fixed point. [1] Let f and g be commuting (g’f=fg) self maps of a complete metric space (X,d) such that f(X) C g(X) and g is continuous. ([11]) Let f and g be compatible self maps of a metric space (X,d).
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