Edelstein-type fixed point theorems in compact TVS-cone metric spaces

Year 2014, Volume: 43 Issue: 4, 561 - 569, 01.08.2014

Thabet Abdeljawad

https://izlik.org/JA35DX64YN

Abstract

In this paper we prove two fixed point theorems in compact cone metric
spaces over normal cones. The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11]. The
second theorem generalizes the main result in [10] and the first theorem.
However, the two theorems fail in different categories. Moreover, different versions of the two theorems are proved in TVS-cone metric spaces
by making use of the nonlinear scalarization function used very recently
by Wei-Shih Du in [A note on cone metric fixed point theory and its
equivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove the
equivalence of the Banach contraction principle in cone metric spaces
and usual metric spaces

Keywords

cone metric , normal cone , strictly normal cone , fixed point , contractive condition. TVS-cone metric space

References

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