Browsing by Author "Park, C"
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Item A new version of Mazur-Ulam theorem under weaker conditions in linear n-normed spacesPark, C; Alaca, CThe 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.Item An introduction to 2-fuzzy n-normed linear spaces and a new perspective to the Mazur-Ulam problemPark, C; Alaca, CThe 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 n-normed linear space or a(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. Mathematics Subject Classification (2010): 03E72; 46B20; 51M25; 46B04; 46S40.Item Mazur-Ulam theorem under weaker conditions in the framework of 2-fuzzy 2-normed linear spacesPark, C; Alaca, CThe 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.Item ORTHOGONAL STABILITY OF AN ADDITIVE-QUADRATIC FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN SPACESLee, JR; Park, C; Alaca, C; Shin, DYUsing the fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-quadratic functional equation 2f (x+y/2) + 2f (x-y/2) = 3/2 f(x) - 1/2 f(y) + 1/2f(-y) (0.1) for all x, y with x perpendicular to y, in non-Archimedean Banach spaces. Here perpendicular to is the orthogonality in the sense of Ratz.Item Fixed point results for modular ultrametric spacesAlaca, C; Ege, ME; Park, CIn 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.Item Stability of additive-quadratic ρ-functional equations in Banach spaces: a fixed point approachPark, C; Kim, SO; Alaca, CLet M(1)f (x, y) : = 3/4 f (x + y) -1/4 f (-x -y) + 1/4 f (x - y) + 1/4 f(y - x) -f (x) -f (y), M(2)f(x, y) : = 2f( x + y/2) + f ( x - y/2 ) + f ( y - x/2 ) -f (x) -f (y). We solve the additive-quadratic rho-functional equations M(1)f (x, y) = rho M(2)f(x, y), (1) and M(2)f(x, y) = rho M(1)f (x, y), (2) where rho is a fixed nonzero number with rho not equal 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive-quadratic rho-functional equations (1) and (2) in Banach spaces. (C)2017 All rights reserved.