Existence and Stability of Best Proximity Point Sets for a New Type of Multivalued Generalized F-Contraction Mappings in Metric Spaces

Let A and B be two nonempty subsets of a metric space (X, d) and CB(X) denote the set of all nonempty closed and bounded subsets of X. Considering the multivalued mappings \(S: A \longrightarrow CB(B)\) and \(\phi : CB(B) \longrightarrow CB(A)\) , we introduce multivalued generalized \(\phi \) -F-contraction mappings. We establish the existence of the best proximity point for such types of mappings in complete metric space. Moreover, we define multivalued generalized \(\phi \) -F-contraction pair of mappings and obtain best proximity point results for these. A stability result is obtained for best proximity point sets, and an analogous study is done for fixed point sets via fixed point formulation for such mappings. Suitable examples are provided in support of defined concepts.