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(2) Any mapping T satisfying the contractive condition (1.3) is a weak contraction.
Any mapping T satisfying the contractive condition (1.3) is a weak contraction.
Any Kannan mapping is a weak contraction.
Corollary 3 [[13], Generalized weak contraction].
Let be a weak contraction with a function.
We give the definition of weak contraction below.
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Sintunavarat and Kumam [5] introduced the notion of generalized (f, α, β -weak contraction to extend the notion of multi-valued (f, α, L)-weak contraction.
Kamran [4] extended these contractions for hybrid pair of mappings and introduced multi-valued (f, θ, L -weak contraction and muL -weakued (f,α,L)-weak contraction.
Later on, Wardowski and Van Dung [18] gave the idea of F-weak contraction and proved a theorem concerning F-weak contraction.
This proves that T is a C-weak contraction on the 2-metric space ( X, d ).
They generalized an F-weak contraction to a generalized F-contraction as follows.
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