Abstract
We introduce the class of generalized -weak contractive set-valued mappings on a metric space. We establish that such mappings have a unique common end point under certain weak conditions. The theorem obtained generalizes several recent results on single-valued as well as certain set-valued mappings.
Highlights
Introduction and PreliminariesAlber and Guerre-Delabriere 1 defined weakly contractive maps on a Hilbert space and established a fixed point theorem for such a map
We introduce the class of generalized ψ, φ -weak contractive set-valued mappings on a metric space
Zhang and Song 5 introduced the concept of a generalized φ-weak contraction condition and obtained a common fixed point for two maps, and −Doric 6 proved a common fixed point theorem for generalized ψ, φ -weak contractions
Summary
Introduction and PreliminariesAlber and Guerre-Delabriere 1 defined weakly contractive maps on a Hilbert space and established a fixed point theorem for such a map. We introduce the class of generalized ψ, φ -weak contractive set-valued mappings on a metric space. We establish that such mappings have a unique common end point under certain weak conditions.
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