Abstract
Common Coupled Fixed Point Theorems for Weakly F-contractive Mappings in Topological Spaces
Highlights
As already known that, if γ : T → T is a ”weakly contractive mapping” for a compact metric space T, γ has a ”fixed point” in T
The above concept was extended by Furi and Vignoli ([8]) to α-condensing mappings acting on a ”bounded complete metric space” which have been generalized by Bugajewski([2]) by make use of the approach of ”weakly F-contractive mappings” acting on a TS
Let {(ct, dt)}t∈Λ be a net in T × T converging to a point (c, d) ∈ T × T
Summary
If γ : T → T is a ”weakly contractive mapping” for a compact metric space T , γ has a ”fixed point” in T (see [7]). Theorem 3.1 Let γ : T × T → T and η : T → T are two commuting mappings on a TS T such that for each countable sets E, F ⊆ T, E = γ( E×F )∪{η(l0)} and F = γ( F ×E)∪{η(m0)} =⇒ E, F are relatively compact where E×F ⊆ E × F, F ×E ⊆ F × E and l0, m0 ∈ T .
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