Alber and Guerre-Delabriere demonstrated the “concept of weak contraction” in 1997. Actually in concept of weak contraction, the authors defined such mappings for single-valued maps on Hilbert spaces and proved the existence of fixed points. Rhoades showed that most results of concept of weak contraction are still true for any Banach space along with that he has proved the following very interesting fixed point theorem which is one of generalizations of the Banach contraction principle because it contains contractions as special cases (ϕ(t)=(1–k)t).
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