Browsing by Author "Bilgili, Nurcan"

Now showing 1 - 6 of 6

Citation - WoS: 14
Citation - Scopus: 23
Cyclic Contractions Via Auxiliary Functions on g-metric Spaces
(Springer international Publishing Ag, 2013) Bilgili, Nurcan; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we prove the existence and uniqueness of fixed points of certain cyclic mappings via auxiliary functions in the context of G-metric spaces, which were introduced by Zead and Sims. In particular, we extend, improve and generalize some earlier results in the literature on this topic.
Citation - WoS: 3
Citation - Scopus: 5
Fixed Point Theorems for Generalized Contractions on gp-metric Spaces
(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Salimi, Peyman; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we present two fixed point theorems on mappings, defined on GP-complete GP-metric spaces, which satisfy a generalized contraction property determined by certain upper semi-continuous functions. Furthermore, we illustrate applications of our theorems with a number of examples. Inspired by the work of Jachymski, we also establish equivalences of certain auxiliary maps in the context of GP-complete GP-metric spaces. MSC: 47H10, 54H25.
Citation - WoS: 25
Citation - Scopus: 27
A Generalization for the Best Proximity Point of Geraghty-Contractions
(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Sadarangani, Kishin; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce the notion of Geraghty-contractions and consider the related best proximity point in the context of a metric space. We state an example to illustrate our result.
Citation - WoS: 36
Citation - Scopus: 38
Generalized α-ψ contractive mappings in quasi-metric spaces and related fixed-point theorems
(Springeropen, 2014) Bilgili, Nurcan; Karapinar, Erdal; Samet, Bessem; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we characterize alpha-psi contractive mappings in the setting of quasi-metric spaces and investigate the existence and uniqueness of a fixed point of such mappings. We notice that by using our result some fixed-point theorems in the context of G-metric space can be deduced.
Citation - WoS: 6
Citation - Scopus: 5
A Note on 'coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces'
(Springer international Publishing Ag, 2014) Bilgili, Nurcan; Erhan, Inci M.; Karapinar, Erdal; Turkoglu, Duran; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Recently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the very recent paper of Turkoglu and Sangurlu 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]' can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result.
Citation - WoS: 28
Citation - Scopus: 33
A Note on Common Fixed Points for (ψ, Α, Β)-Weakly Contractive Mappings in Generalized Metric Spaces
(Springer international Publishing Ag, 2013) Bilgili, Nurcan; Karapinar, Erdal; Turkoglu, Duran; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Very recently, Isik and Turkoglu (Fixed Point Theory Appl. 2013:131, 2013) proved a common fixed point theorem in a rectangular metric space by using three auxiliary distance functions. In this paper, we note that this result can be derived from the recent paper of Lakzian and Samet (Appl. Math. Lett. 25:902-906, 2012).