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Citation - WoS: 35
Citation - Scopus: 46
Some unique fixed point theorems for rational contractions in partially ordered metric spaces
(Springeropen, 2013) Arshad, Muhammad; Karapinar, Erdal; Ahmad, Jamshaid
In this paper, we prove some unique fixed point results for an operator T satisfying certain rational contraction condition in a partially ordered metric space. Our results generalize the main result of Jaggi (Indian J. Pure Appl. Math. 8(2):223-230, 1977). We give several examples to show that our results are proper generalization of the existing one. MSC: 47H10, 54H25, 46J10, 46J15.
Citation - WoS: 5
Citation - Scopus: 5
A Solution for the Non-Cooperative Equilibrium Problem of Two Person Via Fixed Point Theory
(Springeropen, 2015) Tran Duc Thanh; Hobiny, Aatef; Karapinar, Erdal
In this paper, we investigate the non-cooperative equilibrium problem of two person games in the setting of game theory and propose a solution via coupled fixed point results in the context of partial metric spaces. We also realize that our coupled fixed point results can be applied to get a solution of a class of nonlinear Fredholm type integral equations.
Citation - WoS: 5
Citation - Scopus: 14
Existence of a Solution of Integral Equations Via Fixed Point Theorem
(Springeropen, 2013) Gulyaz, Selma; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, Peyman
In 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.
Citation - WoS: 77
Citation - Scopus: 81
α-admissible mappings and related fixed point theorems
(Springeropen, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Akbar, Farhana
In 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.
Citation - WoS: 8
Citation - Scopus: 12
On Almost Contractions in Partially Ordered Metric Spaces via Implicit Relations
(Springeropen, 2012) Gul, Ugur; Karapinar, Erdal
In this paper, we prove general fixed point theorems for self-maps of a partially ordered complete metric space which satisfy an implicit type relation. Our method relies on constructive arguments involving Picard type iteration processes and our uniqueness result uses comparability arguments. Our results generalize a multitude of fixed point theorems in the literature to the context of partially ordered metric spaces.
Citation - WoS: 3
Citation - Scopus: 5
Fixed Point Theorems for Generalized Contractions on gp-metric Spaces
(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Salimi, Peyman
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: 22
Citation - Scopus: 29
Fixed point results for generalized (α, ψ)-Meir-Keeler contractive mappings and applications
(Springeropen, 2014) Latif, Abdul; Gordji, Madjid Eshaghi; Karapinar, Erdal; Sintunavarat, Wutiphol
In this paper, we introduce a new type of a generalized-(alpha, psi)-Meir-Keeler contractive mapping and establish some interesting theorems on the existence of fixed points for such mappings via admissible mappings. Applying our results, we derive fixed point theorems in ordinary metric spaces and metric spaces endowed with an arbitrary binary relation.
Citation - WoS: 25
Citation - Scopus: 27
A Generalization for the Best Proximity Point of Geraghty-Contractions
(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Sadarangani, Kishin
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: 15
Citation - Scopus: 20
A Short Note on c*-valued Contraction Mappings
(Springeropen, 2016) Alsulami, Hamed H.; Agarwal, Ravi P.; Karapinar, Erdal; Khojasteh, Farshid
In this short note we point out that the recently announced notion, the C*-valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C*-valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.
Citation - WoS: 4
Citation - Scopus: 5
A Note on '(g, f)-closed Set and Tripled Point of Coincidence Theorems for Generalized Compatibility in Partially Metric Spaces'
(Springeropen, 2014) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco
Recently, some (common) multidimensional fixed theorems in partially ordered complete metric spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we realized 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 results included in the very recent paper (Charoensawan and Thangthong in Fixed Point Theory Appl. 2014:245, 2014) can be considered as a consequence of existing fixed point theorems on the topic in the literature.

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