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Article Citation - WoS: 4Citation - Scopus: 3Existence of solutions of integral equations via fixed point theorems(Springeropen, 2014) Gulyaz, Selma; Erhan, Inci M.Existence and uniqueness of fixed points of a mapping defined on partially ordered G-metric spaces is discussed. The mapping satisfies contractive conditions based on certain classes of functions. The results are applied to the problems involving contractive conditions of integral type and to a particular type of initial value problems for the nonhomogeneous heat equation in one dimension. This work is a generalization of the results published recently in (Gordji et al. in Fixed Point Theory Appl. 2012:74, 2012, doi:10.1186/1687-1812-2012-74) to G-metric space.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: 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: 5Citation - Scopus: 14Existence of a Solution of Integral Equations Via Fixed Point Theorem(Springeropen, 2013) Gulyaz, Selma; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, PeymanIn this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.Article Citation - WoS: 77Citation - Scopus: 81α-admissible mappings and related fixed point theorems(Springeropen, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Akbar, FarhanaIn this paper, we prove the existence and uniqueness of a fixed point for certain alpha-admissible contraction mappings. Our results generalize and extend some well-known results on the topic in the literature. We consider some examples to illustrate the usability of our results.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: 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: 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: 22Citation - Scopus: 29Fixed point results for generalized (α, ψ)-Meir-Keeler contractive mappings and applications(Springeropen, 2014) Latif, Abdul; Gordji, Madjid Eshaghi; Karapinar, Erdal; Sintunavarat, WutipholIn this paper, we introduce a new type of a generalized-(alpha, psi)-Meir-Keeler contractive mapping and establish some interesting theorems on the existence of fixed points for such mappings via admissible mappings. Applying our results, we derive fixed point theorems in ordinary metric spaces and metric spaces endowed with an arbitrary binary relation.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.
