Browsing by Author "Turkoglu, Duran"

Now showing 1 - 4 of 4

Citation - WoS: 6
Citation - Scopus: 5
Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces
(Univ Osijek, dept Mathematics, 2011) Turkoglu, Duran; Abdeljawad, Thabet; Abuloha, Muhib; Abdeljawad, Thabet; Matematik
In this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ciric in [8, 27] are recovered.
Citation - WoS: 39
Citation - Scopus: 50
Kkm Mappings in Cone Metric Spaces and Some Fixed Point Theorems
(Pergamon-elsevier Science Ltd, 2010) Abuloha, Muhib; Abdeljawad, Thabet; Turkoglu, Duran
In this paper, we define KKM mappings in cone metric spaces and define NR-cone metric spaces to obtain some fixed point theorems and hence generalize the results obtained in [A. Amini, M. Fakhar, J. Zafarani, KKM mapping in metric spaces, Nonlinear Anal. 60 (2005) 1045-1052]. (C) 2009 Elsevier Ltd. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 2
Locally Convex Valued Rectangular Metric Spaces and the Kannan's Fixed Point Theorem
(Eudoxus Press, Llc, 2012) Abdeljawad, Thabet; Abdeljawad, Thabet; Turkoglu, Duran; Matematik
Rectangular TVS-cone metric spaces are introduced and Kannan's fixed point theorem is proved in these spaces. Two approaches are followed for the proof. At first we prove the theorem by a direct method using the structure of the space itself. Secondly, we use the nonlinear scalarization used 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. The proof is done without any normality assumption on the cone of the locally convex topological vector space, and hence generalizing several previously obtained results.
Citation - WoS: 35
Some Theorems and Examples of Cone Banach Spaces
(Eudoxus Press, Llc, 2010) Abdeljawad, Thabet; Abdeljawad, Thabet; Turkoglu, Duran; Abuloha, Muhib; Matematik
In this paper, by defining a cone norm parallel to.parallel to(A) on E over itself which behaves like the absolute value norm on R, we construct examples of cone Banach spaces. Namely, we define the m-Euclidian cone normed space E-m, E-infinity and the space C-E(S) of continuous functions in cones, to generalize the Banach spaces R-m, l(infinity) and C [a, b], respectively. Some basic lemmas and theorems are also proved to help in the construction and in the proof of completeness of the above mentioned examples of cone normed spaces.