Browsing by Author "Sadarangani, Kishin"

Now showing 1 - 7 of 7

Citation Count: 8
Berinde Mappings in Ordered Metric Spaces
(Springer-verlag Italia Srl, 2015) Karapinar, Erdal; Karapınar, Erdal; Sadarangani, Kishin; Mathematics
Recently, 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.
Citation Count: 9
Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions
(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Karapınar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, Kishin; Mathematics
The 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.
Citation Count: 65
Fixed Point Theory for Cyclic (i•-Ψ)
(Springer international Publishing Ag, 2011) Karapinar, Erdal; Karapınar, Erdal; Sadarangani, Kishin; Mathematics
In this article, the concept of cyclic (I center dot - psi)-contraction and a fixed point theorem for this type of mappings in the context of complete metric spaces have been presented. The results of this study extend some fixed point theorems in literature. 2000 Mathematics Subject Classification: 47H10;46T99 54H25.
Citation Count: 4
Fixed point theory for cyclic weak φ-contraction (vol 24, pg 822, 2011)
(Pergamon-elsevier Science Ltd, 2012) Karapınar, Erdal; Sadarangani, Kishin; Mathematics
We 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.
Citation Count: 25
A Generalization for the Best Proximity Point of Geraghty-Contractions
(Springeropen, 2013) Bilgili, Nurcan; Karapınar, Erdal; Karapinar, Erdal; Sadarangani, Kishin; Mathematics
In 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.
Citation Count: 17
A Note on Best Proximity Point Theorems under Weak P-Property
(Hindawi Publishing Corporation, 2014) Karapınar, Erdal; Karapinar, Erdal; Sadarangani, Kishin; Mathematics
In the very recent paper of Akbar and Gabeleh (2013), by using the notion of P-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weak P-property.
Citation Count: 1
TRIPLE FIXED POINT THEOREMS FOR WEAK (ψ-φ)-CONTRACTIONS
(Eudoxus Press, Llc, 2013) Karapınar, Erdal; Sadarangani, Kishin; Mathematics
The 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.