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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: 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: 91Citation - Scopus: 110New Extension of p-metric Spaces With Some Fixed-Point Results on m-metric Spaces(Springer international Publishing Ag, 2014) Asadi, Mehdi; Karapinar, Erdal; Salimi, PeymanIn this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings.Article Citation - WoS: 23Citation - Scopus: 35A new approach to G-metric and related fixed point theorems(Springer, 2013) Asadi, Mehdi; Karapinar, Erdal; Salimi, PeymanVery recently, Samet et al. and Jleli and Samet reported that most of fixed point results in the context of G-metric space, defined by Sims and Zead, can be derived from the usual fixed point theorems on the usual metric space. In this paper, we state and prove some fixed point theorems in the framework of G-metric space that cannot be obtained from the existence results in the context of associated metric space.
