Abstract:
Let X be a Banach space, K a
nonempty closed subset of X and let
T,S:K → X be two nonself almost contractions. In this paper, we prove the existence of coincidence points and common fixed
points of almost contractions T and S. The main result shows that if S(K) is closed,
the pair (T,S) has property (
M') and T and S satisfy some suitable conditions,
then T and S have a unique common fixed point in K. This theorem
generalizes several fixed point theorems for nonself mappings and also extend many great results in the fixed point theory of self mappings to the case on
nonself mappings. Also, we give an example to support the validity of our results.
Key Words: Banach space, nonself almost contraction, weakly compatible mapping, coincidence point, common fixed point, property (
M').
2010 Mathematics Subject Classification: Primary 47H10. Secondary 47H09, 54H25.
