Meir-Keeler \(\alpha\)-contractive fixed and common fixed point theorems (Q395212)

In the paper [\textit{B. Samet} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No.\ 4, 2154--2165 (2012; Zbl 1242.54027)], \(\alpha\)-admissible and \(\alpha\)-contractive mappings were introduced and some fixed point results for such mappings were proved. The present author introduces Meir-Keeler-type (generalized) \(\alpha\)-contractions and proves a common fixed point theorem for a pair of \(\alpha\)-admissible contractions of this type on an orbitally complete metric space. The result is applied to prove the existence of coupled fixed points.