Dr. Mortaza Abtahi
Assistant Professor
Suzuki-type fixed point theorems for generalized contractive mappings that characterize metric completeness
| Abstract | |
| Inspired by the work of Suzuki in [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861–1869], we prove a fixed point theorem for contractive mappings that generalizes a theorem of Geraghty in [M.A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604–608] and characterizes metric completeness. We introduce the family A of all nonnegative functions ϕ with the property that, given a metric space (X,d) and a mapping T:X→X, the condition |