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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