@article{article_530162, title={Edelstein-type fixed point theorems in compact TVS-cone metric spaces}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={43}, pages={561–569}, year={2014}, author={Abdeljawad, Thabet}, keywords={cone metric,normal cone,strictly normal cone,fixed point,contractive condition. TVS-cone metric space}, abstract={<div style="text-align: justify;"> <span style="font-size: 0.9em;">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 </span> </div>}, number={4}, publisher={Hacettepe University}