Double Controlled Metric Type Spaces and Some Fixed Point Results

By Thabet Abdeljawad, Nabil Mlaiki, Hassen Aydi, N. Souayah. Mathematics, 2018

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In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) ≤ α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z ∈ X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces.

Subfields: Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1d81a95eb0291c0ea955e5eb3ae343e93443d2a9