Abstract
The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results.
Highlights
Introduction and PreliminariesIt will be almost 100 years since S
Banach gave us one of the most beautiful achievements in the intellectual activity of modern man. This is his theorem proved in his doctoral dissertation in 1922. Recall this famous accomplishment: Each mapping T of the complete metric space ( X, d) into itself, if it satisfies the condition that there exists λ ∈ [0, 1) such that d( Tω, TΩ) ≤ λd(ω, Ω), (1)
Denote by Ψ the set of all functions ψ : [0, +∞) → [0, +∞) so that ψ is continuous and ψ (t) = 0 if and only t = 0. Under this new set-up, Piri and Kumam introduced and established the following Wardowski and Suzuki type fixed point results in b-metric spaces
Summary
Introduction and PreliminariesIt will be almost 100 years since S. By adding the following four new values θ T 2 Ω, Ω , θ T 2 Ω, TΩ , θ T 2 Ω, ω , θ T 2 Ω, Tω to a contraction condition, Dung and Hang ([44]) proved some fixed point theorems.
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