Research Article
Year 2014,
Volume: 43 Issue: 4, 561 - 569, 01.08.2014
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
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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There are 1 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Mathematics |
| Authors | |
| Publication Date | August 1, 2014 |
| Published in Issue | Year 2014 Volume: 43 Issue: 4 |