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Article Common Fixed Point Theorem for Three Mappings in Banach Valued Norm Spaces(Gazi Univ, 2013) Karapinar, Erdal; Moradlou, Fridoun; Salimi, Peyman; MathematicsIn this paper, we give a generalized theorem on point of coincidence and common fixed point for three weakly compatible mappings in Banach valued norm spaces. We give a new method for construction of the sequence, which is convergence to the common fixed point of these three mappings.Article Citation - WoS: 5Citation - Scopus: 14Existence of a Solution of Integral Equations Via Fixed Point Theorem(Springeropen, 2013) Gulyaz, Selma; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, PeymanIn this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.Article Citation - WoS: 77Citation - Scopus: 81α-admissible mappings and related fixed point theorems(Springeropen, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Akbar, FarhanaIn this paper, we prove the existence and uniqueness of a fixed point for certain alpha-admissible contraction mappings. Our results generalize and extend some well-known results on the topic in the literature. We consider some examples to illustrate the usability of our results.Article Citation - WoS: 3Citation - Scopus: 5Fixed Point Theorems for Generalized Contractions on gp-metric Spaces(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Salimi, PeymanIn 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.Article Citation - WoS: 10Citation - Scopus: 11Fixed Point Theorems Via Auxiliary Functions(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Salimi, PeymanWe prove new fixed point theorems in the framework of partially ordered metric spaces. The main result is an extension and a generalization of many existing results in the literature. An example is also considered to illustrate the main result.Article Citation - WoS: 61Citation - Scopus: 81Dislocated metric space to metric spaces with some fixed point theorems(Springer international Publishing Ag, 2013) Karapinar, Erdal; Salimi, PeymanIn this paper, we notice the notions metric-like space and dislocated metric space are exactly the same. After this historical remark, we discuss the existence and uniqueness of a fixed point of a cyclic mapping in the context of metric-like spaces. We consider some examples to illustrate the validity of the derived results of this paper.Article Citation - WoS: 203Citation - Scopus: 268On α-ψ< Contractive Mappings(Springer international Publishing Ag, 2013) Karapinar, Erdal; Kumam, Poom; Salimi, PeymanIn this paper, we introduce the notion of alpha-psi-Meir-Keeler contractive mappings via a triangular alpha-admissible mapping. We discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces. We state a number of examples to illustrate our results. MSC: 46N40, 47H10, 54H25, 46T99.Article Citation - WoS: 23Citation - Scopus: 35A new approach to G-metric and related fixed point theorems(Springer, 2013) Asadi, Mehdi; Karapinar, Erdal; Salimi, PeymanVery recently, Samet et al. and Jleli and Samet reported that most of fixed point results in the context of G-metric space, defined by Sims and Zead, can be derived from the usual fixed point theorems on the usual metric space. In this paper, we state and prove some fixed point theorems in the framework of G-metric space that cannot be obtained from the existence results in the context of associated metric space.Article Citation - WoS: 12Citation - Scopus: 15Some Fixed Point Results in gp-metric Spaces(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Salimi, Peyman; Karapnar, ErdalFollowing a recent paper of Zand and Nezhad (2011), we establish some fixed point results in GP-metric spaces. The presented theorems generalize and improve several existing results in the literature. Also, some examples are presented.Article Citation - WoS: 48Citation - Scopus: 46Fixed Point Results for gm< Contractive and g-(α, Ψ)-Meir Contractive Mappings(Springer international Publishing Ag, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Vetro, PasqualeIn this paper, first we introduce the notion of a G(m)-Meir-Keeler contractive mapping and establish some fixed point theorems for the G(m)-Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a G(c)(m)-Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(alpha, psi)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.
