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A generalized Suzuki-Berinde contraction that characterizes Banach spaces

Abbas Mujahid, Anjum Rizwan, Rakočević Vladimir

Journal of Applied Analysis

2023

Vol. 29, nr 2

239--250

We introduce a large class of contractive mappings, called Suzuki-Berinde type contraction. We show that any Suzuki-Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature.