[PDF] Top 20 Mazur-Ulam theorem in probabilistic normed groups
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Mazur-Ulam theorem in probabilistic normed groups
... Theorem 2.5. Suppose that (G, F, µ) and (G 0 , F 0 , τ ) are two probabilistic normed groups such that both G, G 0 are uniquely 2-divisible abelian groups. Let the conditions (C1), (C2) ... See full document
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A Mazur Ulam problem in non Archimedean n normed spaces
... In this section, we introduce a non-Archimedean n-normed space which is a kind of gener- alization of a non-Archimedean -normed space, and we show the (additive) Mazur-Ulam theorem for ... See full document
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Stability of mappings on multi normed spaces
... 1940, Ulam [22] first raised the stability problem of functional equations: ‘For which metric groups G is it true that an ε-automorphism of G is necessarily near to an automorphism?’ In the next year, Hyers ... See full document
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Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces
... general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear ... See full document
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The Aleksandrov problem in quasi convex n-normed linear spaces
... for all x, y ∈ E, where d E (, ) and d F (, ) denote the metric in the space E and F, respectively. For some fixed number r > 0, suppose that f preserves distance r; ie, for all x, y ∈ E with d E (x, y) = r, we have d ... See full document
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On the Mazur Ulam problem in non Archimedean fuzzy 2 normed spaces
... Theorem . Let X and Y be non-Archimedean fuzzy -normed spaces over a linear or- dered non-Archimedean field K with C = { n |n ∈ Z}. Let X and Y be strict convexities. Sup- pose that f : X −→ Y is a fuzzy ... See full document
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Mazur Ulam theorem under weaker conditions in the framework of 2 fuzzy 2 normed linear spaces
... the Mazur-Ulam theorem on probabilistic - normed ...the Mazur-Ulam theorem in non-Archimedean ...the Mazur-Ulam problem on non-Archimedean ... See full document
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The extensions of isometries between the 2-dimensional normed spaces
... the Mazur-Ulam theorem by different patterns, and have paid attention to weaken the condition of the Mazur-Ulam theorem from different ...the Mazur-Ulam ... See full document
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An introduction to 2 fuzzy n normed linear spaces and a new perspective to the Mazur Ulam problem
... the Mazur-Ulam theorem, that is, when X is a 2-fuzzy n - normed linear space or ℑ ( X ) is a fuzzy n -normed linear space, the Mazur-Ulam theorem ... See full document
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The Hyers Ulam Rassias stability of the quartic functional equation in fuzzy β normed spaces
... In the next year, Hyers [] gave a positive answer to the above question for additive groups under the assumption that the groups are Banach spaces. In , Rassias [] ex- tended the theorem of ... See full document
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Generalized Ulam Hyers Stability of Jensen Functional Equation in Šerstnev PN Spaces
... It is easy to see that f with f0 0 satisfies the Jensen equation if and only if it is additive; compare for 39, Theorem 6. Stability of Jensen equation has been studied at first by Kominek 36 and then by several ... See full document
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Approximately generalized additive functions in several variables via fixed point method
... Aoki-Rolewicz Theorem [54], each quasi-norm is equivalent to some p-norm (see also [7]) Since it is much easier to work with p-norms, henceforth we restrict our attention mainly to ...Hyers-Rassias-Gajda ... See full document
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Orthogonal Stability of Mixed Additive Quadratic Jensen Type Functional Equation in Multi Banach Spaces
... The notion of multi-normed space is introduced by Dales and Polyakov [17]. This concept is somewhat simi- lar to operator sequence space and has some connections with operator spaces and Banach lattices. ... See full document
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On locally convex probabilistic normed spaces
... Probabilistic normed spaces (briefly, PN spaces) were introduced by Šerstnev [] by means of a definition that was closely modeled in the theory of normed ...and probabilistic ... See full document
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Stability of functional equations in \((n,\beta)\) normed spaces
... 2. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 3. Rassias, TM: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297-300 ... See full document
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A proof of the Mazur-Orlicz theorem via the Markov-Kakutani common fixed point theorem, and vice versa
... the Mazur-Orlicz theorem and its generalizations in the ...point theorem is new and ...point theorem was used to prove the Hahn-Banach ...the Mazur-Orlicz theorem, the authors of ... See full document
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On Nonlinear Equations for -Contractor Couple in Fuzzy Normed Spaces
... existence theorem of solutions for set-valued nonlinear operator equations in fuzzy normed ...existence theorem to prove a new fixed point theorem in fuzzy normed ... See full document
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Daneš theorem in complete random normed modules
... random normed module is a random generalization of an ordinary normed ...ordinary normed spaces, random normed modules possess the rich strat- ification structure, which is introduced in this ... See full document
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Ulam-Hyers Stability of Additive and Reciprocal Functional Equations: Direct and Fixed Point Methods
... S.M. Ulam [47] introduced the stability of functional ...the Ulam question for Banach spaces. In 1978, Hyers theorem was generalized by ...the Ulam stability problem for different mappings ... See full document
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On α Šerstnev probabilistic normed spaces
... For the reader’s convenience, now we recall the most recent definition of a Probabil- istic Normed space (briefly, a PN space) [5]. It is also the definition adopted in this article and became the standard one, ... See full document
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