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Article Citation - WoS: 178Citation - Scopus: 184Couple fixed point theorems for nonlinear contractions in cone metric spaces(Pergamon-elsevier Science Ltd, 2010) Karapinar, ErdalThe notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham (2006) in [13]. In this manuscript, some results of Lakshmikantham and Ciric (2009) in [5] are extended to the class of cone metric spaces. (C) 2010 Elsevier Ltd. All rights reserved.Article Citation - WoS: 59Citation - Scopus: 67Generalized (c)-conditions and Related Fixed Point Theorems(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Tas, KenanIn this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 70Citation - Scopus: 68Best Proximity Points of Cyclic Mappings(Pergamon-elsevier Science Ltd, 2012) Karapinar, ErdalIn this this manuscript, we proved that the existence of best proximity points for the cyclic operators T defined on a union of subsets A, B of a uniformly convex Banach space X with T (A) subset of B, T(B) subset of A and satisfying the condition parallel to Tx - Yy parallel to <= alpha/3[parallel to x-y parallel to + parallel to Tx - x parallel to + parallel to Ty - y parallel to] + (1 - alpha)diam(A, B) for alpha is an element of (0, 1) and for all x is an element of A, for all y is an element of B, where diam(A, B) = inf{parallel to x - y parallel to : x is an element of A, y is an element of B}. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 173Fixed Point Theory for Cyclic Weak Φ-Contraction(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Karapınar, Erdal; Karapınar, Erdal; Mathematics; MathematicsIn this manuscript, the notion of cyclic weak phi-contraction is considered. It is shown that a self-mapping T on a complete metric space X has a fixed point if it satisfied cyclic weak phi-contraction. (C) 2010 Elsevier Ltd. All rights reserved.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.
