Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces
Mustafa Aslantaş
2021Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics22 citationsDOIOpen Access PDF
Abstract
In this paper, we first introduce a new notion of the property (M_{C}) to improve and generalize the property (G_{C}). After that, we present two new concepts, proximal b-cyclic contraction of first type and second type, on b-metric spaces. Then, we obtain two best proximity point results for such mappings in the frameworks of best proximally complete b-metric spaces by using the property (M_{C}). Hence, we generalize some results existing in the literature. Finally, we present some illustrative and interesting examples.
Topics & Concepts
Metric spaceProperty (philosophy)MathematicsContraction (grammar)Point (geometry)Metric mapMetric (unit)Pure mathematicsType (biology)Discrete mathematicsConvex metric spaceGeometryEngineeringMedicineInternal medicineEpistemologyOperations managementPhilosophyBiologyEcologyFixed Point Theorems AnalysisSpatial and Cultural Studies