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Article Citation - WoS: 69Citation - Scopus: 70An Approach To Best Proximity Points Results Via Simulation Functions(Springer Basel Ag, 2017) Karapinar, Erdal; Khojasteh, FarshidIn this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.Article Citation - WoS: 56Best Proximity Point on Different Type Contractions(Natural Sciences Publishing Corp-nsp, 2011) Karapinar, Erdal; Erhan, Inci M.In this manuscript, some proximity points are obtained by using different types cyclic contractions. Also, generalized cyclic Meir Keeler contraction is introduced and a new fixed point theorem for this cyclic mapping is stated.Article Citation - WoS: 9Citation - Scopus: 8Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, KishinThe main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.Article Citation - WoS: 4Best Proximity Point for Certain Proximal Contraction Type Mappings(Univ Prishtines, 2018) Alqahtani, Badr; Hamzehnejadi, Javad; Karapinar, Erdal; Lashkaripour, RahmatollahIn this paper, we introduce the new notion of generalized proximal alpha-h-phi-contraction mappings and investigate the existence of the best proximity point for such mappings in the complete metric spaces.
