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Article Citation - WoS: 6Citation - Scopus: 5A Note on 'coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces'(Springer international Publishing Ag, 2014) Bilgili, Nurcan; Erhan, Inci M.; Karapinar, Erdal; Turkoglu, DuranRecently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed 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 very recent paper of Turkoglu and Sangurlu 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]' can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result.Conference Object Citation - WoS: 2Citation - Scopus: 1Rational Forms That Imply the Uniqueness of Fixed Points in Partial Metric Spaces(Yokohama Publ, 2019) Karapinar, Erdal; MathematicsIn this paper, we investigate the existence and uniqueness of fixed points of Jaggi type contractions by using a simulation function in the framework of partial metric spaces. Our results improve, extend and unify several results on the topic in the literature.Article Citation - WoS: 23Citation - Scopus: 31A Discussion on "α-Ψ Contraction Type Mappings "(Univ Nis, Fac Sci Math, 2014) Karapinar, ErdalIn this paper we discuss the subadditivity property of some auxiliary functions which have been used to generalize the contractive conditions on maps. Our results show that this property is not required in many cases and therefore, can be removed. We emphasize that in several papers (see e.g.[1]-[11]) dealing with such contraction mappings, the hypotheses of the main theorems can be restated in the light of our results.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: 172Citation - Scopus: 190Interpolative 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: 35Citation - Scopus: 46Some unique fixed point theorems for rational contractions in partially ordered metric spaces(Springeropen, 2013) Arshad, Muhammad; Karapinar, Erdal; Ahmad, JamshaidIn 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.Article Citation - WoS: 17Citation - Scopus: 27Fixed Point Theorems in New Generalized Metric Spaces(Springer Basel Ag, 2016) Karapinar, Erdal; Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; Karapınar, Erdal; Mathematics; MathematicsThe aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.Article Citation - WoS: 6Citation - Scopus: 10On Quasi-Contraction Mappings of Ciric and Fisher Type Via ω-distance(Natl inquiry Services Centre Pty Ltd, 2019) Darko, Kocev; Karapinar, Erdal; Rakocevic, VladimirKada, Suzuki, and Takahashi introduced and studies the concept of omega- distance in fixed point theory. In this paper, we generalize and unify Ciric' and Fisher fixed points results for quasi-contractions on metric space to omega-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in metric spaces.Article Citation - WoS: 1Citation - Scopus: 5A Note on Recent Fixed Point Results Involving g-quasicontractive Type Mappings in Partially Ordered Metric Spaces(Springer international Publishing Ag, 2014) Karapinar, Erdal; Samet, BessemIn this note, we establish the equivalence between recent fixed point theorems involving quasicontractive type mappings in metric spaces endowed with a partial order.Article Citation - WoS: 6Citation - Scopus: 7A Note on Fixed Point Results in Complex-Valued Metric Spaces(Springer international Publishing Ag, 2015) Al-Mezel, Saleh A.; Alsulami, Hamed H.; Karapinar, Erdal; Khojasteh, FarshidIn this paper, we prove that the fixed point results in the context of complex-valued metric spaces can be obtained as a consequence of corresponding existing results in the literature in the setting of associative metric spaces. In particular, we deduce that any complex metric space is a special case of cone metric spaces with a normal cone.
