Browsing by Author "Aydi, Hassen"

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Advances on Multivalued Operators and Related Fixed Point Problems
(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Du, Wei-Shih; Aydi, Hassen; Romaguera, Salvador; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
[No Abstract Available]
Citation - WoS: 23
Citation - Scopus: 32
Berinde-Type Generalized Contractions on Partial Metric Spaces
(Hindawi Ltd, 2013) Aydi, Hassen; Amor, Sana Hadj; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We consider generalized Berinde-type contractions in the context of partial metric spaces. Such contractions are also known as generalized almost contractions in the literature. In this paper, we extend, generalize, and enrich the results in this direction. Some examples are presented to illustrate our results.
Citation - WoS: 24
Citation - Scopus: 29
Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems
(Springer int Publ Ag, 2013) Kumam, Poom; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, Wutiphol; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem.
Citation - WoS: 21
Citation - Scopus: 23
Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self
(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, Peyman; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.
Citation - WoS: 198
A COMMON FIXED POINT FOR WEAK φ-CONTRACTIONS ON b-METRIC SPACES
(House Book Science-casa Cartii Stiinta, 2012) Aydi, Hassen; Bota, Monica-Felicia; Karapinar, Erdal; Moradi, Sirous; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we give a common fixed point result, for single-valued and multi-valued mappings satisfying a weak phi-contraction in b-metric spaces. Presented theorems extend, generalize and improve some existing results in the literature. Some examples are also given.
Citation - WoS: 40
Citation - Scopus: 35
Common Fixed Points for Generalized -Implicit Contractions in Partial Metric Spaces: Consequences and Application
(Springer-verlag Italia Srl, 2015) Aydi, Hassen; Jellali, Manel; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce the concept of generalized -admissible pair of mappings generalizing the definition of -admissible mappings presented by Samet et al. (Nonlinear Anal 75:2154-2165, 2012). Based on above, we define generalized -implicit contractions in the setting of partial metric spaces and we provide some common fixed point results for such contractions. We also derive some consequences and corollaries from our obtained results. An application and some examples are presented making effective the new concepts and results.
Citation - WoS: 90
Citation - Scopus: 95
Common Fixed Points for Single-Valued and Multi-Valued Maps Satisfying a Generalized Contraction in -Metric Spaces
(Springer int Publ Ag, 2012) Tahat, Nedal; Aydi, Hassen; Karapinar, Erdal; Shatanawi, Wasfi; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this article, we establish some common fixed point theorems for a hybrid pair {} of single valued and multi-valued maps satisfying a generalized contractive condition defined on -metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. 54H25; 47H10; 54E50.
Citation - WoS: 11
Citation - Scopus: 8
Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions
(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We prove coupled coincidence point and coupled fixed point results of F : X x X -> X and g : X -> X involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.
Citation - WoS: 19
Citation - Scopus: 14
Coupled coincidence point results on generalized distance in ordered cone metric spaces
(Springer, 2013) Aydi, Hassen; Karapinar, Erdal; Mustafa, Zead; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via -distance. We also proved some related coupled common fixed point theorems for such mappings. Our results generalize, extend, and unify several well-known comparable results in the literature regarding this topic. We present some examples to illustrate the concepts and results.
Citation - WoS: 20
Citation - Scopus: 49
Coupled Coincidence Points in Partially Ordered Cone Metric Spaces With a c-distance
(Hindawi Ltd, 2012) Shatanawi, Wasfi; Karapinar, Erdal; Aydi, Hassen; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Cho et al. (2012) proved some coupled fixed point theorems in partially ordered cone metric spaces by using the concept of a c-distance in cone metric spaces. In this paper, we prove some coincidence point theorems in partially ordered cone metric spaces by using the notion of a c-distance. Our results generalize several well-known comparable results in the literature. Also, we introduce an example to support the usability of our results.
Citation - WoS: 143
Citation - Scopus: 141
Coupled Fixed Point Results for (ψ, Φ)-Weakly Contractive Condition in Ordered Partial Metric Spaces
(Pergamon-elsevier Science Ltd, 2011) Aydi, Hassen; Karapinar, Erdal; Shatanawi, Wasfi; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we prove some coupled fixed point theorems involving a (psi, phi)-weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces. These results are analogous to theorems of Van Luong and Xuan Thuan (2011) [10] on the class of ordered partial metric spaces. Also, an application is given to support our results. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 43
Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces
(Hindawi Ltd, 2012) Abdeljawad, Thabet; Aydi, Hassen; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F : X x X -> X and g : X -> X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012)
Citation - WoS: 27
Citation - Scopus: 24
A Discussion on Generalized Almost Contractions Via Rational Expressions in Partially Ordered Metric Spaces
(Springeropen, 2014) Mustafa, Zead; Karapinar, Erdal; Aydi, Hassen; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The main purpose of this paper is to give some fixed point results for mappings involving generalized (phi, psi)-contractions in partially ordered metric spaces. Our results generalize, extend, and unify several well-known comparable results in the literature (Jaggi in Indian J. Pure Appl. Math. 8(2):223-230, 1977, Harjani et al. in Nonlinear Anal. 71:3403-3410, 2009, Luong and Thuan in Fixed Point Theory Appl. 2011:46, 2011). The presented results are supported by three illustrative examples.
Citation - WoS: 78
Citation - Scopus: 63
Discussion on Some Coupled Fixed Point Theorems
(Springer international Publishing Ag, 2013) Samet, Bessem; Karapinar, Erdal; Aydi, Hassen; Rajic, Vesna Cojbasic; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we show that, unexpectedly, most of the coupled fixed point theorems (on ordered metric spaces) are in fact immediate consequences of well-known fixed point theorems in the literature. MSC: 47H10, 54H25.
Citation - WoS: 6
Citation - Scopus: 6
Existence of Solutions for a Periodic Boundary Value Problem Via Generalized Weakly Contractions
(Hindawi Ltd, 2013) Moradi, Sirous; Karapinar, Erdal; Aydi, Hassen; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We discuss the existence of solutions for a periodic boundary value problem and for some polynomials. For this purpose, we present some fixed point theorems for weakly and generalized weakly contractive mappings in the setting of partially ordered complete metric spaces.
Citation - WoS: 15
FIXED POINT RESULTS FOR GENERALIZED α-ψ-CONTRACTIONS IN METRIC-LIKE SPACES AND APPLICATIONS
(Texas State Univ, 2015) Aydi, Hassen; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this article, we introduce the concept of generalized alpha-psi-contraction in the context of metric-like spaces and establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some examples and an application on two-point boundary value problems for second order differential equation are also considered.
Citation - WoS: 28
Citation - Scopus: 34
Fixed Point Results on a Class of Generalized Metric Spaces
(Springer Heidelberg, 2012) Aydi, Hassen; Karapinar, Erdal; Lakzian, Hossein; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Brianciari ('A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,' Publ. Math. Debrecen 57 (2000) 31-37) initiated the notion of the generalized metric space as a generalization of a metric space in such a way that the triangle inequality is replaced by the 'quadrilateral inequality,' d(x, y) <= d(x, a) + d(a, b) + d(b, y) for all pairwise distinct points x, y, a, and b of X. In this paper, we establish a fixed point result for weak contractive mappings T : X -> X in complete Hausdorff generalized metric spaces. The obtained result is an extension and a generalization of many existing results in the literature.
Citation - WoS: 233
Citation - Scopus: 265
A fixed point theorem for set-valued quasi-contractions in b-metric spaces
(Springer international Publishing Ag, 2012) Aydi, Hassen; Bota, Monica-Felicia; Karapinar, Erdal; Mitrovic, Slobodanka; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.
Citation - WoS: 8
Citation - Scopus: 8
Fixed Point Theorems for Various Classes of Cyclic Mappings
(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Samet, Bessem; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We introduce new classes of cyclic mappings and we study the existence and uniqueness of fixed points for such mappings. The presented theorems generalize and improve several existing results in the literature.
Citation - WoS: 62
Citation - Scopus: 76
Fixed Points for Generalized (α, Ψ)-Contractions on Generalized Metric Spaces
(Springeropen, 2014) Aydi, Hassen; Karapinar, Erdal; Samet, Bessem; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we introduce some generalized (alpha, psi)-contractive mappings in the setting of generalized metric spaces and, based on the very recent paper (Kirk and Shahzad in Fixed Point Theory Appl. 2013:129, 2013), we omit the Hausdorff hypothesis to prove some fixed point results involving such mappings. Some consequences on existing fixed point theorems are also derived.