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Article Citation - WoS: 3On Ciric Type φ-Geraghty Contractions(Chiang Mai Univ, Fac Science, 2019) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper we introduce the notions of phi-Geraghty contractions and Ciric type phi-Geraghty contractions. We also investigate under which conditions such mappings posses a unique fixed point in the framework of complete metric spaces. We consider examples to show the validity of our main results.Article Citation - WoS: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn 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.Article Citation - WoS: 57Citation - Scopus: 74Further Fixed Point Results on g-metric Spaces(Springer int Publ Ag, 2013) Karapinar, Erdal; Agarwal, Ravi P.Very recently, Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) noticed that some fixed point theorems in the context of a G-metric space can be deduced by some well-known results in the literature in the setting of a usual (quasi) metric space. In this paper, we note that the approach of Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) is inapplicable unless the contraction condition in the statement of the theorem can be reduced into two variables. For this purpose, we modify some existing results to suggest new fixed point theorems that fit with the nature of a G-metric space. The expressions in our result, the contraction condition, cannot be expressed in two variables, therefore the techniques used in (Int. J. Anal. 2013: 917158, 2013; Fixed Point Theory Appl. 2012: 210, 2012) are not applicable.Article Citation - WoS: 3Citation - Scopus: 4A New Class of Generalized Contraction Using p-functions in Ordered Metric Spaces(Sciendo, 2015) Amor, Sana Hadj; Karapinar, Erdal; Kumam, PoomIn this paper, we introduced and studied a new class of mappings in ordered metric spaces that is inspired from the concept of a P-function introduced in Chaipunya et. al. [10]. With our new class, we furnish fixed point theorems for continuous, noncontinuous, monotonic, and nonmonotonic mappings in various kinds of the ordering structures.Article Citation - WoS: 60Citation - Scopus: 72Remarks on some coupled fixed point theorems in G-metric spaces(Springer international Publishing Ag, 2013) Agarwal, Ravi P.; Karapinar, ErdalIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems in the context of (ordered) G-metric spaces are in fact immediate consequences of usual fixed point theorems that are either well known in the literature or can be obtained easily.Article Citation - WoS: 57Citation - Scopus: 71Fixed Point Theorems for Α-Geraghty Contraction Type Maps in Metric Spaces(Springer int Publ Ag, 2013) Cho, Seong-Hoon; Bae, Jong-Sook; Karapinar, ErdalIn this paper, we introduce a notion of alpha-Geraghty contraction type maps in the setting of a metric space. We also establish some fixed point theorems for such maps and give an example to illustrate our results. Finally, we discuss the application of our main results in the research fields of ordinary differential equations.Article Citation - WoS: 31Citation - Scopus: 43On Best Proximity Point of Ψ-Geraghty Contractions(Springer international Publishing Ag, 2013) Karapinar, ErdalVery recently, Caballero, Harjani and Sadarangani (Fixed Point Theory Appl. 2012: 231, 2012) observed some best proximity point results for Geraghty contractions by using the P-property. In this paper, we introduce the notion of psi-Geraghty contractions and show the existence and uniqueness of the best proximity point of such contractions in the setting of a metric space. We state examples to illustrate our result.Article Citation - WoS: 29Citation - Scopus: 42Mixed g-monotone Property and Quadruple Fixed Point Theorems in Partially Ordered Metric Spaces(Springer international Publishing Ag, 2012) Mustafa, Zead; Aydi, Hassen; Karapinar, ErdalIn this manuscript, we prove some quadruple coincidence and common fixed point theorems for F : X-4 -> X and g : X -> X satisfying generalized contractions in partially ordered metric spaces. Our results unify, generalize and complement various known results from the current literature. Also, an application to matrix equations is given.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: 5Citation - Scopus: 6Revisiting of Some Outstanding Metric Fixed Point Theorems Via e-contraction(Ovidius Univ Press, 2018) Fulga, Andreea; Karapinar, ErdalIn this paper, we introduce the notion of alpha-psi-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.
