Browsing by Author "Alaca 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 and an application to homotopy in modular metric spaces(International Scientific Research Publications, 2015) Ege M.E.; Alaca C.The purpose of this paper is to define new concepts, such as T-orbitally w-completeness, orbitally w- continuity and almost weakly w-contractive mapping in the modular metric spaces. We prove some fixed point theorems for these related concepts and mappings in this space. Further, we give an application using the technique in [Lj. B. Ćirić, B. Samet, H. Aydi, C. Vetro, Appl. Math. Comput., 218 (2011), 2398-2406] and show that our results can be applied to homotopy. © 2015 All rights reserved.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 Some properties of modular S-metric spaces and its fixed point results(Eudoxus Press, LLC, 2016) Ege M.E.; Alaca C.In this paper, we introduce modular S-metric spaces and deal with their some properties. We also prove some fixed point theorems on complete modular S-metric spaces. © 2016 Eudoxus Press, LLC. All rights reserved.Item Some results for modular b-metric spaces and an application to system of linear equations(Azerbaijan Mathematical Society, 2018) Ege M.E.; Alaca C.In this paper, we define the modular b-metric space with some new notions and prove Banach fixed point theorem and its two generalizations for the new space. At the end of the paper, we give an application of Banach contraction principle to a system of linear equations. © 2010 AZJM All rights reserved.Item Cytogenetic effects of c6h4 (Ch3)2 (xylene) on meristematic cells of root tips of vicia faba l. and mathematical analysis(Firenze University Press, 2020) Alaca C.; Özdemir A.; Bozdağ B.; Özdemir C.Xylene is a readily flammable and poisonous liquid with a chemical formula of C6H4 (CH3)2. It is used as raw material or auxiliary raw material in many industrial products such as dye, pencil, agricultural chemicals, rubber, fiber, glue and diaper. In this study, cytogenetic effects of xylene, on the meristematic cells of root tips of V. faba L. used as food have been investigated. For this purpose, the seeds of the plant have been treated with xylene solutions prepared in different concentrations for different time periods. Chromosomes at the root tips have been looked and the effect of xylene has been determined. The abnormalities as chromosome breaking, chromosome dispersion, bridge chromosome, chromosome adherence, ring chromosome have been observed. Abnormalities have been seen at each treatment depended on the time periods. In addition to these visible damages of xylene in the study, possible damages on chromosomes carrying genetic codes of living beings to future generations have been investigated and mathematical analyzes has been made. The results obtained have been evaluated statistically. © 2020 C. Alaca, A. Özdemir, B. Bozdağ, C. Özdemir.Item SOME COMMON FIXED POINT THEOREMS IN Ϝ-METRIC SPACES(SCIK Publishing Corporation, 2020) Bozkus B.; Alaca C.In this paper, we prove a new common fixed point theorem for four mappings in Ϝ-metric spaces and give its results. Our main results are Ϝ-metric version of Fisher’s main theorems [5] and [6]. Furthermore, our main result is a generalization of Theorem 4 in [12]. © 2020 the author(s).