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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: 15
Citation - Scopus: 21
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.
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: 30
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: 5
Citation - Scopus: 7
Irremissible Stimulate on 'unified Fixed Point Theorems in Fuzzy Metric Spaces Via Common Limit Range Property'
(Springeropen, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Kumam, Poom
One of the goals of this short note is to alert researchers as regards some mistakes that appeared in a recent paper (Chauhan, Khan and Kumar in J. Inequal. Appl. 2013: 182, 2013). This entails main proofs based on a false result, which invalidates all statements. We also give a complete revision of the antecedents of this work in order to find the main reasons of the mistakes. Finally, the main aim of this note is to propose a correct, more general version of the main theorems in the paper mentioned.
Citation - WoS: 97
Citation - Scopus: 148
Further Generalizations of the Banach Contraction Principle
(Springeropen, 2014) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem
We establish a new fixed point theorem in the setting of Branciari metric spaces. The obtained result is an extension of the recent fixed point theorem established in Jleli and Samet (J. Inequal. Appl. 2014: 38, 2014).

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