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Article Citation - WoS: 15Citation - Scopus: 21A Short Note on c*-valued Contraction Mappings(Springeropen, 2016) Alsulami, Hamed H.; Agarwal, Ravi P.; Karapinar, Erdal; Khojasteh, FarshidIn this short note we point out that the recently announced notion, the C*-valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C*-valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.Article Citation - WoS: 8Citation - Scopus: 12On Almost Contractions in Partially Ordered Metric Spaces via Implicit Relations(Springeropen, 2012) Gul, Ugur; Karapinar, ErdalIn this paper, we prove general fixed point theorems for self-maps of a partially ordered complete metric space which satisfy an implicit type relation. Our method relies on constructive arguments involving Picard type iteration processes and our uniqueness result uses comparability arguments. Our results generalize a multitude of fixed point theorems in the literature to the context of partially ordered metric spaces.Article Citation - WoS: 13Citation - Scopus: 18A note on some coupled fixed-point theorems on G-metric spaces(Springeropen, 2012) Ding, Hui-Sheng; Karapinar, ErdalThe purpose of this paper is to extend some recent coupled fixed-point theorems in the context of G-metric space by essentially different and more natural way. We state some examples to illustrate our results.Article Citation - Scopus: 1Some Remarks About the Existence of Coupled g-coincidence Points(Springeropen, 2015) Erhan, Inci M.; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, NaseerVery recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps.Article Citation - WoS: 3Citation - Scopus: 5Fixed Point Theorems for Generalized Contractions on gp-metric Spaces(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Salimi, PeymanIn this paper, we present two fixed point theorems on mappings, defined on GP-complete GP-metric spaces, which satisfy a generalized contraction property determined by certain upper semi-continuous functions. Furthermore, we illustrate applications of our theorems with a number of examples. Inspired by the work of Jachymski, we also establish equivalences of certain auxiliary maps in the context of GP-complete GP-metric spaces. MSC: 47H10, 54H25.Article Citation - WoS: 25Citation - Scopus: 27A Generalization for the Best Proximity Point of Geraghty-Contractions(Springeropen, 2013) Bilgili, Nurcan; Karapinar, Erdal; Sadarangani, KishinIn this paper, we introduce the notion of Geraghty-contractions and consider the related best proximity point in the context of a metric space. We state an example to illustrate our result.Article Citation - WoS: 29Citation - Scopus: 34A New Approach To (α, Ψ)-Contractive Nonself Multivalued Mappings(Springeropen, 2014) Ali, Muhammad Usman; Kamran, Tayyab; Karapinar, ErdalIn this paper, we introduce the notions of alpha-admissible and alpha-psi-contractive type condition for nonself multivalued mappings. We establish fixed point theorems using these new notions along with a new condition. Moreover, we have constructed examples to show that our new condition is different from the corresponding existing conditions in the literature.Article Citation - WoS: 16Citation - Scopus: 16Lyapunov Type Inequalities for Even Order Differential Equations With Mixed Nonlinearities(Springeropen, 2015) Agarwal, Ravi P.; Ozbekler, AbdullahIn the case of oscillatory potentials, we present Lyapunov and Hartman type inequalities for even order differential equations with mixed nonlinearities: x((2n))(t) + (-1)(n-1) Sigma(m)(i=1) q(i)(t)vertical bar x(t)vertical bar(alpha i-1) x(t) = 0, where n,m epsilon N and the nonlinearities satisfy 0 < alpha(1) < center dot center dot center dot < alpha(j) < 1 < alpha(j+1) < center dot center dot center dot < alpha(m) < 2.Article Citation - WoS: 5Citation - Scopus: 5A Solution for the Non-Cooperative Equilibrium Problem of Two Person Via Fixed Point Theory(Springeropen, 2015) Tran Duc Thanh; Hobiny, Aatef; Karapinar, ErdalIn this paper, we investigate the non-cooperative equilibrium problem of two person games in the setting of game theory and propose a solution via coupled fixed point results in the context of partial metric spaces. We also realize that our coupled fixed point results can be applied to get a solution of a class of nonlinear Fredholm type integral equations.Article Citation - WoS: 14Citation - Scopus: 25On Coupled Fixed Point Theorems on Partially Ordered g-metric Spaces(Springeropen, 2012) Karapinar, Erdal; Kaymakcalan, Billur; Tas, KenanIn this manuscript, we extend, generalize and enrich some recent coupled fixed point theorems in the framework of partially ordered G-metric spaces in a way that is essentially more natural.
