Abstract
In this research paper, we have set some related fixed point results for generalized weakly contractive mappings defined in partially ordered complete b -metric spaces. Our results are an extension of previous authors who have already worked on fixed point theory in b -metric spaces. We state some examples and one sample of the application of the obtained results in integral equations, which support our results.
Highlights
The concept of b-metric space has been dealt with by distinctly different authors since it first appeared and became largely used
Roshan et al [7] used the notion of almost generalized contractive mappings in ordered complete b-metric spaces and set some fixed and common fixed point results
We have obtained interesting results on the coupled fixed point theorems that give a generalization of well-known results in the field
Summary
The concept of b-metric space has been dealt with by distinctly different authors since it first appeared and became largely used. We consider four self-mappings f , g, P, and T in ordered complete two b-metric space ðX, d, δ, ≼Þ that fulfill the following conditions: (i) ff , gg is dominated and fP, Tg is dominating (ii) f X ⊆ TX and gX ⊆ PX (iii) ψ ∈ Ψ, φ ∈ Φ and for every two comparable elements x, y ∈ X, we have ψÀs4 dð f x, Á gyÞ
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