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Article Citation - WoS: 29Citation - Scopus: 36Fixed 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: 9Citation - Scopus: 12Some Integral Type Common Fixed Point Theorems Satisfying Φ-Contractive Conditions(Belgian Mathematical Soc Triomphe, 2014) Chauhan, Sunny; Karapinar, ErdalIn this manuscript, we obtain some common fixed point results of two pairs having the common limit range property in the setting of integral type contraction in the framework of symmetric (semi-metric) spaces. Moreover, we extend our results from two pairs of self-mappings to four finite families of self mappings to get common fixed points. Our results improve and extend a host of previously known results. Further, we establish some illustrative examples to show the validity of the main results.Article Citation - WoS: 21Citation - Scopus: 23On (α, Ψ)-k-contractions in the Extended b-metric Space(Univ Nis, Fac Sci Math, 2018) Alqahtani, Badr; Karapinar, Erdal; Ozturk, AliIn this paper, we introduce a notion of (alpha, psi)-K-contraction in the setting of extended b-metric spaces and investigate the existence of a fixed point. The presented results generalize and unify a number of well-known fixed point theorem mainly in two distinct aspects; in the sense of the contraction conditions and in the frame of abstract spaces.Article Citation - WoS: 15Citation - Scopus: 15A Note on 'ψ-geraghty Type Contractions'(Springer international Publishing Ag, 2014) Karapinar, Erdal; Samet, BessemVery recently, the notion of a psi-Geraghty type contraction was defined by Gordji et al. (Fixed Point Theory and Applications 2012: 74, 2012). In this short note, we realize that the main result via psi-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. in (Fixed Point Theory and Applications 2012:74, 2012) can be derived in the same way.Article Citation - WoS: 43A Common Fixed Point Theorem for Cyclic Operators on Partial Metric Spaces(Univ Nis, Fac Sci Math, 2012) Karapinar, Erdal; Karapınar, Erdal; Shobkolaei, Nabi; Sedghi, Shaban; Vaezpour, S. Mansour; Karapınar, Erdal; Mathematics; MathematicsIn this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.Article Citation - WoS: 13Citation - Scopus: 16A 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) 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: 15Contractive Multivalued Maps in Terms of q-functions on Complete Quasimetric Spaces(Springer international Publishing Ag, 2014) Karapinar, Erdal; Romaguera, Salvador; Tirado, PedroIn this paper we prove the existence of a fixed point for multivalued maps satisfying a contraction condition in terms of Q-functions, and via Bianchini-Grandolfi gauge functions, for complete T-0-quasipseudometric spaces. Our results extend, improve, and generalize some recent results in the literature. We present some examples to validate and illustrate our results.Article Citation - WoS: 15Fixed Point Results for Various Α-Admissible Contractive Mappings on Metric-Like Spaces(Hindawi Ltd, 2014) Al-Mezel, Saleh A.; Chen, Chi-Ming; Karapinar, Erdal; Rakocevic, VladimirWe establish some fixed point theorems for alpha-admissible mappings in the context of metric-like space via various auxiliary functions. In particular, we prove the existence of a fixed point of the generalized Meir-Keeler type alpha-phi-contractive self-mapping.. defined on a metric- like space X. The given results generalize, improve, and unify several fixed point theorems for the generalized cyclic contractive mappings that have appeared recently in the literature.Article Citation - WoS: 176Citation - Scopus: 194Interpolative Reich-Rus Type Contractions on Partial Metric Spaces(Mdpi, 2018) Karapinar, Erdal; Agarwal, Ravi; Aydi, HassenBy giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85-87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich-Rus-Ciric in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121-124; Boll. Unione Mat. Ital. 1972, 4, 26-42 and Boll. Unione Mat. Ital. 1971, 4, 1-11.) is not applicable.Article Citation - WoS: 27Citation - Scopus: 28Generalized Meir-Keeler Type Contractions on g-metric Spaces(Elsevier Science inc, 2013) Mustafa, Zead; Aydi, Hassen; Karapinar, ErdalIn this manuscript, we introduce generalized Meir-Keeler type contractions over G-metric spaces. Moreover, we show that every orbitally continuous generalized Meir-Keeler type contraction has a unique fixed point on complete G-metric spaces. We illustrate our results by some given examples. (C) 2013 Elsevier Inc. All rights reserved.
