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Fixed point theorems on orthogonal metric spaces via altering distance functions
(Maltepe Üniversitesi, 2019) Bilgili Güngör, Nurcan; Turkoglu, Duran
In 1984, Khan et al. [3] established some fixed point theorems in complete and compact metric spaces by using altering distance functions. In 2017, Gordji et al. [2] described the notion of orthogonal set and orthogonal metric spaces. In their work, they held an generalization of Banach fixed point theorem in this interesting defined construction and in addition, applied their acquired results to demonstrate the existence of a solution of an ordinary differential equation. In this paper, some fixed point theorems on orthogonal metric spaces via altering distance functions are presented inspired by [3] and [2].
Some fixed point results on modular f-metric spaces
(Maltepe Üniversitesi, 2019) Manav, Nesrin; Turkoglu, Duran
Jleli and Samet(2018)[8] introduced a new concept, named a F-metric space, as a generalization of the notion of metric space. In this paper, we compare the topology produced by modular metric and by modular F-metric and cover some useful properties of this topology for fixed point theorems in future studies. Then, we prove Banach contraction principle in modular F-metric spaces.