Some New Observations on Generalized Contractive Mappings and Related Results in b-Metric-Like Spaces

Abstract

Abstract: In this paper, we consider, discuss, complement, improve, generalize, and enrich some fixed point results obtained for (β − ψ1 − ψ2)−contractive conditions in ordered b-metric-like spaces. By using our new approach for the proof that one Picard’s sequence is bbl−Cauchy in the context of b-metric-like spaces, we get much shorter proofs than the ones mentioned in the recent papers. Also, by the use of our method, we complement and enrich some common fixed point results for β: s,ψ, q,ϕ−contraction mappings. Our approach in this paper generalizes and modifies several comparable results in the existing literature.