Browsing by Author "Park C."
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Item An introduction to 2-fuzzy n-normed linear spaces and a new perspective to the mazur-ulam problem(2012) Park C.; Alaca C.The purpose of this article is to introduce the concept of 2-fuzzy n-normed linear space or fuzzy n-normed linear space of the set of all fuzzy sets of a non-empty set. We define the concepts of n-isometry, n-collinearity n-Lipschitz mapping in this space. Also, we generalize the Mazur-Ulam theorem, that is, when X is a 2-fuzzy nnormed linear space or ℑ(X) is a fuzzy n-normed linear space, the Mazur-Ulam theorem holds. Moreover, it is shown that each n-isometry in 2-fuzzy n-normed linear spaces is affine. © 2012 Park and Alaca.Item Orthogonal stability of an additive-quadratic functional equation in non-archimedean spaces(2012) Lee J.R.; Park C.; Alaca C.; Shin D.Y.Using the fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-quadratic functional equation, for all x, y with x ⊥ y, in non-Archimedean Banach spaces. Here ⊥ is the orthogonality in the sense of Rätz. © 2012 EUDOXUS PRESS, LLC.Item Mazur-Ulam theorem under weaker conditions in the framework of 2-fuzzy 2-normed linear spaces(2013) Park C.; Alaca C.The purpose of this paper is to prove that every 2-isometry without any other conditions from a fuzzy 2-normed linear space to another fuzzy 2-normed linear space is affine, and to give a new result of the Mazur-Ulam theorem for 2-isometry in the framework of 2-fuzzy 2-normed linear spaces. © 2013 Park and Alaca; licensee Springer.Item A new version of Mazur-Ulam theorem under weaker conditions in linear n-normed spaces(Eudoxus Press, LLC, 2014) Park C.; Alaca C.Abstract: The purpose of this paper is to prove a new result of Mazur-Ulam theorem for n-isometry without any other conditions in linear n-normed spaces. © 2014 EUDOXUS PRESS, LLC.Item Fixed point results for modular ultrametric spaces(Eudoxus Press, LLC, 2016) Alaca C.; Ege M.E.; Park C.In this study, we define the notion of modular ultrametric space. We present a fixed point theorem in modular spherically complete ultrametric space, and prove coincidence point theorem for three self maps in a modular spherically complete ultrametric space. © 2016 by Eudoxus Press, LLC, All rights reserved.Item Fixed point theorems for various contraction conditions in digital metric spaces(Eudoxus Press, LLC, 2019) Park C.; Ege O.; Kumar S.; Jain D.; Lee J.R.In this paper, we prove the existence of fixed points for Kannan contraction, Chatterjea contraction and Reich contraction in setting of digital metric spaces. These digital contractions are the applications of metric fixed point theory contractions. © 2019 by Eudoxus Press, LLC,all rights reserved.