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Öğe Some related fixed point theorems for multivalued mappings on two metric spaces(Vasyl Stefanyk Precarpathian National University, 2020) Biçer, Özge; Olgun, Murat; Alyıldız, Turhan; Altun, İshakThe definition of related mappings was introduced by Fisher in 1981. He proved some theorems about the existence of fixed points of single valued mappings defined on two complete metric spaces and relations between these mappings. In this paper, we present some related fixed point results for multivalued mappings on two complete metric spaces. First we give a classical result which is an extension of the main result of Fisher to the multivalued case. Then considering the recent technique of Wardowski, we provide two related fixed point results for both compact set valued and closed bounded set valued mappings via F-contraction type conditions.Öğe A related fixed point theorem for F-contractions on two metric spaces(Hacettepe University, 2019) Olgun, Murat; Biçer, Özge; Alyıldız, Tuğçe; Altun, İshakRecently, Wardowski in [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012] introduced the concept of F-contraction on complete metric space which is a proper generalization of Banach contraction principle. In the present paper, we proved a related fixed point theorem with F-contraction mappings on two complete metric spaces.Öğe Banach contraction crinciple in cone modular spaces with banach algebra(Afyon Kocatepe University, 2019) Özavşar, Muttalip; Çay, HaticeThere are some mappings, which are not contraction mappings in the usual senses, such that they hold some contractive type conditions in the settings of some new abstract metric and modular spaces. In this paper, taking into account this fact, we introduce such a new type modular space by using the setting of cones in Banach algebras. In the first section, some basic notions and definitions are given. In the second part, it is shown that some result of Banach Contraction Principle in modular space with ....-algebra is equal to the result of Banach Contraction Principle of the usual modular space. Then that new modular space mentioned above is introduced and some results are given. Finally the work is concluded with an example.Öğe Fixed point results for F-contractions on space with two metrics(University of Niš Faculty of Science and Mathematics, 2017) Olgun, Murat; Alyıldız, Tuğçe; Biçer, Özge; Altun, İshakIn this paper, taking into account two metrics on a space, we present a new fixed point theorem for F-contractions. Our theorem includes both Agarwal and O'Regan's and Wardowski's results as properly. Also we provide a nontrivial example showing this fact.
