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Metric fixed-point theory lies in the intersection of three main subjects: topology, functional analysis, and applied mathematics. The first fixed-point theorem, also known as contraction mapping principle, was abstracted by Banach from the papers of Liouville and Picard, in which certain differential equations were solved by using the method of successive approximation. In other words, fixed-point theory developed from applied mathematics and has developed in functional analysis and topology. Fixed-point theory is a dynamic research subject that has never lost the attention of researchers, as it is very open to development both in theoretical and practical fields. In this Special Issue, among several submissions, we selected eight papers that we believe will be interesting to researchers who study metric fixed-point theory and related applications. It is great to see that this Special Issue fulfilled its aims. There are not only theoretical results but also some applications that were based on obtained fixed-point results. In addition, the presented results have great potential to be improved, extended, and generalized in distinct ways. The published results also have a wide application potential in various qualitative sciences, including physics, economics, computer science, engineering, and so on.

Research & information: general --- Mathematics & science --- b-metric --- Banach fixed point theorem --- Caristi fixed point theorem --- homotopy --- M-metric --- M-Pompeiu–Hausdorff type metric --- multivalued mapping --- fixed point --- quasi metric space --- altering distance function --- (ψ, ϕ)-quasi contraction. --- pata type contraction --- Suzuki type contraction --- C-condition --- orbital admissible mapping --- non-Archimedean quasi modular metric space --- θ-contraction --- Suzuki contraction --- simulation contraction --- R-function --- simulation function --- manageable function --- contractivity condition --- binary relation --- quasi-metric space --- left K-complete --- α–ψ-contractive mapping --- asymptotic stability --- differential and riemann-liouville fractional differential neutral systems --- linear matrix inequality --- b-metric --- Banach fixed point theorem --- Caristi fixed point theorem --- homotopy --- M-metric --- M-Pompeiu–Hausdorff type metric --- multivalued mapping --- fixed point --- quasi metric space --- altering distance function --- (ψ, ϕ)-quasi contraction. --- pata type contraction --- Suzuki type contraction --- C-condition --- orbital admissible mapping --- non-Archimedean quasi modular metric space --- θ-contraction --- Suzuki contraction --- simulation contraction --- R-function --- simulation function --- manageable function --- contractivity condition --- binary relation --- quasi-metric space --- left K-complete --- α–ψ-contractive mapping --- asymptotic stability --- differential and riemann-liouville fractional differential neutral systems --- linear matrix inequality