Common Fixed Points for Hybrid Pair of Maps with CLR-Property in Convex Metric Space - Dhingra, Kusum; Rathee, Savita (Communications in Mathematics and Applications, 2020)
In present work, we prove common fixed point theorem and best proximity point theorem for two pairs of hybrid mappings in convex metric space satisfying \((ψ-φ)\)-contractive conditions under common limit range property with respect to \(q\). We prove both theorems for two pairs of hybrid mappings which can be utilized to derive common fixed point and best proximity point theorem including any number of finite mappings. We also present an example to support our main result.
Keywords: Convex metric space; Common limit range property; Common fixed point; Best proximity point; Compatible maps; q-affine; pq-affine