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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14411/18
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Article Citation - WoS: 14Citation - Scopus: 17A Remark on "existence and Uniqueness for a Neutral Differential Problem With Unbounded Delay Via Fixed Point Results F-Metric Spaces"(Springer-verlag Italia Srl, 2019-05-14) Aydi, Hassen; Karapinar, Erdal; Mitrovic, Zoran D.; Rashid, TawseefVery recently, Hussain and Kanwal (Trans A Razmadze Math Inst 172(3): 481-490, 2018) proved some (coupled) fixed point results in this setting for a -.-contractive mappings on the setting of F-metric spaces that was initiated by Jleli and Samet (Fixed Point Theory Appl 2018: 128, 2018). In this note, we underline that the proof of Hussain and Kanwal (Trans A Razmadze Math Inst 172(3): 481-490, 2018) has a gap. We provide two examples to illustrate our observation. We also correct the proof and improved the result by replacing a-admissibility by orbital a-admissibility.Article Citation - WoS: 13Citation - Scopus: 15Best Proximity Point Results in Dislocated Metric Spaces Via <i>r</I>-functions(Springer-verlag Italia Srl, 2017-09-05) Gholizadeh, Leila; Karapinar, ErdalIn this paper, we investigate the existence of best proximity of R-contractions in the frame of dislocated metric spaces. We also propose some conditions to guarantee the uniqueness of best proximity point for such contractions. We consider an illustrative example to support the given results. This result generalizes a number of recent results on the topic in the literature.Article Citation - WoS: 37Citation - Scopus: 36A Fixed Point Theorem and the Ulam Stability in Generalized Dq-Metric Spaces(Academic Press inc Elsevier Science, 2018-11) Brzdek, Janusz; Karapinar, Erdal; Petrusel, AdrianWe prove a fixed point theorem for function spaces, that is a very efficient and convenient tool for the investigations of various operator inequalities connected to Ulam stability issues, in classes of functions taking values in various spaces (e.g., in ultrametric spaces, dq-metric spaces, quasi-Banach spaces, and p-Banach spaces). The theorem is a natural generalization and extension of the classical Banach Contraction Principle and some other more recent results. (C) 2018 Elsevier Inc. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 54Common Fixed Point Results on an Extended B-Metric Space(Springeropen, 2018-07-03) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we investigate the existence of common fixed points of a certain mapping in the frame of an extended b-metric space. The given results cover a number of well-known fixed point theorems in the literature. We state some examples to illustrate our results.Article Citation - WoS: 1Citation - Scopus: 1Discussion on the Fixed Point Problems With Constraint Inequalities(Springeropen, 2018-08-30) Alqahtani, Badr; Lashkaripour, Rahmatollah; Karapinar, Erdal; Hamzehnejadi, JavadIn this paper, we introduce the concept of comparable complete metric spaces and consider some fixed point theorems for mappings in the setting of incomplete metric spaces. We obtain the results of Ansari et al. [J. Fixed Point Theory Appl. 20:26, 2018] with weaker conditions. Moreover, we provide some corollaries and examples show that our main result is a generalization of existing results in the literature.Article Citation - WoS: 16Citation - Scopus: 16Fixed Points of Weakly Compatible Mappings Satisfying Generalized Φ-Weak Contractions(Malaysian Mathematical Sciences Soc, 2014-12-17) Vetro, Calogero; Chauhan, Sunny; Karapinar, Erdal; Shatanawi, WasfiIn this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a phi-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature.Article Citation - WoS: 9Citation - Scopus: 10Last Remarks on <i>g</I>-metric Spaces and Related Fixed Point Theorems(Springer-verlag Italia Srl, 2015-08-06) Agarwal, Ravi P.; Karapinar, Erdal; Roldan Lopez de Hierro, Antonio FranciscoIn this report, we present some new fixed points theorems in the context of quasi-metric spaces that can be particularized in a wide range of different frameworks (metric spaces, partially ordered metric spaces, G-metric spaces, etc.). Our contractivity conditions involve different classes of functions and we study the case in which they only depend on a unique variable. Furthermore, we do not only introduce new contractivity conditions, but also expansivity conditions. As a consequence of our results, we announce that many fixed point results in G-metric spaces can be derived from the existing results if all arguments are not distinct.Article Citation - WoS: 30Citation - Scopus: 37Fixed Point Results on a Class of Generalized Metric Spaces(Springer Heidelberg, 2012) Aydi, Hassen; Karapinar, Erdal; Lakzian, HosseinBrianciari ('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.Article Citation - WoS: 41Citation - Scopus: 44Some New Fixed Point Theorems in Fuzzy Metric Spaces(Ios Press, 2014-01) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Manro, SaurabhThe aim of this paper is to introduce a new class of contractive mappings such as fuzzy alpha-psi-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.Article Citation - WoS: 15Citation - Scopus: 16On Cyclic (ψ, Φ)-Contractions in Kaleva-seikkala's Type Fuzzy Metric Spaces(Ios Press, 2014) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemIn this paper we introduce the notion of cyclic (psi, phi)-contractions on fuzzy metric spaces in the sense of Kaleva and Seikkala, and we discuss the existence and uniqueness of fixed points for mappings satisfying such type of contractions.