Double-Composed Metric Spaces

The double-controlled metric-type space (X,D) is a metric in which the triangle inequality has form D(η,μ)≤ζ1(η,θ)D(η,θ)+ζ2(θ,μ)D(θ,μ) for all η,θ,μ∈X. maps ζ1,ζ2:X×X→[1,∞) are called control functions. In this paper, we introduce novel generalization of double-composed space, where D(η,μ)≤αD(η,θ)+βD(θ,μ) our new functions α,β:[0,∞)→[0,∞) composed D inequality, multiplied with D. We establish some fixed-point theorems along examples and applications.