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Citation - WoS: 12
Citation - Scopus: 18
On the existence of fixed points that belong to the zero set of a certain function
(Springer international Publishing Ag, 2015) Karapinar, Erdal; O'Regan, Donal; Samet, Bessem
Let T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem.
Citation - WoS: 4
On common fixed points that belong to the zero set of a certain function
(int Scientific Research Publications, 2017) Karapinar, Erdal; Samet, Bessem; Shahi, Priya
We provide sufficient conditions under which the set of common fixed points of two self-mappings f, g : X -> X is nonempty, and every common fixed point of f and g is the zero of a given function phi : X -> [0, infinity). Next, we show the usefulness of our obtained result in partial metric fixed point theory. (C) 2017 All rights reserved.