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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: 1TRIPLE FIXED POINT THEOREMS FOR WEAK (ψ-φ)-CONTRACTIONS(Eudoxus Press, Llc, 2013) Karapinar, Erdal; Sadarangani, KishinThe notion of coupled fixed point is introduced in by Bhaskar and Lakshmikantham in [2]. Very recently, the concept of the tripled fixed point is introduced by Berinde and Borcut [1]. They also proved some triple fixed point theorems. In this manuscript, by using the weak (psi - phi)-contraction, the results of Berinde and Borcut [1] are generalized.Article Citation - WoS: 8Citation - Scopus: 8Berinde Mappings in Ordered Metric Spaces(Springer-verlag Italia Srl, 2015) Karapinar, Erdal; Sadarangani, KishinRecently, Samet and Vetro proved a fixed point theorem for mappings satisfying a general contractive condition of integral type in orbitally complete metric spaces (Samet and Vetro, Chaos Solitons Fractals 44:1075-1079, 2011). Our aim in this paper is to present a version of the results obtained in the above mentioned paper in the context of ordered metric spaces. Some examples are presented to distinguish our results from the existing ones.Correction Citation - WoS: 4Citation - Scopus: 12Fixed point theory for cyclic weak φ-contraction (vol 24, pg 822, 2011)(Pergamon-elsevier Science Ltd, 2012) Karapinar, Erdal; Sadarangani, KishinWe correct the proof of Theorem 6 in the letter "Fixed point theory for cyclic weak phi-contraction" [E. Karapinar, Fixed point theory for cyclic weak phi-contraction, Appl. Math. Lett. 24 (6) (2011) 822-825]. (C) 2010 Elsevier Ltd. All rights reserved.
