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Citation - WoS: 32
Citation - Scopus: 45
Fixed Point Theorems for a Class of Α-Admissible Contractions and Applications To Boundary Value Problem
(Hindawi Publishing Corporation, 2014) Alsulami, Hamed H.; Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.
A class of alpha-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.
Citation - WoS: 3
Citation - Scopus: 3
An Illusion: "a Suzuki Type Coupled Fixed Point Theorem"
(Hindawi Publishing Corporation, 2014) Alsulami, Hamed H.; Karapinar, Erdal; Kutbi, Marwan A.; Roldan-Lopez-de-Hierro, Antonio-Francisco
We admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014)] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Doric and Lazovic (2011)] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (alpha, r)-admissible contractions.