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Random Normed Spaces

On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces

On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces

... Every solution of the quadratic functional equation is said to be a quadratic mapping. The stability problem for the quadratic functional equation first was proved by J. M. Rassias 12 for mappings f : X → Y, where X is a ...

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On nonlinear stability in various random normed spaces

On nonlinear stability in various random normed spaces

... of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory ...

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A functional equation related to inner product spaces in non Archimedean L random normed spaces

A functional equation related to inner product spaces in non Archimedean L random normed spaces

... of random normed spaces (RN-spaces) is important as a generalization of the deterministic result of linear normed spaces and also in the study of random operator ...fuzzy ...

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Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces

Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces

... In the sequel we adopt the usual terminology, notations, and conventions of the theory of random normed spaces, as in 19–21. Throughout this paper, Δ is the space of distribution functions that is, ...

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Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces

Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces

... metric spaces, which is then used to obtain stability properties for different kinds of functional equations linear functional equations, generalized equation of the square root, spiral generalized gamma equations ...

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On the Stability of a General Mixed Additive Cubic Functional Equation in Random Normed Spaces

On the Stability of a General Mixed Additive Cubic Functional Equation in Random Normed Spaces

... in random normed spaces and derive from it results on stability of equation f4x 10f2x − ...of random normed ...the random normed spaces, which correspond, for ...

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Stability of functional inequalities in matrix random normed spaces

Stability of functional inequalities in matrix random normed spaces

... In the sequel, we adopt the usual terminology, notations and conventions of the theory of random normed spaces, as in [–]. Throughout this paper, + is the space of dis- tribution functions, that ...

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On the stability of an AQCQ functional equation in random normed spaces

On the stability of an AQCQ functional equation in random normed spaces

... In the sequel, we adopt the usual terminology, notations and conventions of the the- ory of random normed spaces, as in [35-37]. Throughout this paper, Δ + is the space of distribution functions, ...

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Erratum to: A Note to Paper "On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces"

Erratum to: A Note to Paper "On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces"

... solution of the cubic functional equation is said to be a cubic mapping. The stability problem for the cubic functional equation was solved by Jun and Kim 2 and Lee 3 for mappings f : X → Y , where X is a real ...

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On the Stability of Functional Equations in Random Normed Spaces

On the Stability of Functional Equations in Random Normed Spaces

... f (x+3y)3 f (x + y)+3 f (xy) f (x3y) =48 f (y) (1.1) is said to be the cubic functional equation since f (x) = cx 3 is its solution. Every solution of the cubic functional equation is said to be a cubic mapping. The ...

10

Approximately generalized additive functions
in several variables

Approximately generalized additive functions in several variables

... in random normed spaces, RN-spaces and fuzzy normed spaces has been recently studied in, Alsina [3], Mirmostafaee, Mirzavaziri and Moslehian [50, 51, 52], Mihet¸ and Radu ...

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Mazur-Ulam theorem in probabilistic normed groups

Mazur-Ulam theorem in probabilistic normed groups

... real normed spaces is affine ...in normed and metric groups [3, 10] and in probabilistic and random normed spaces [1, ...

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Approximately generalized additive functions in several variables via fixed point method

Approximately generalized additive functions in several variables via fixed point method

... of random normed spaces (RN-spaces) is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ...in ...

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On generalized double statistical convergence in a random 2 normed space

On generalized double statistical convergence in a random 2 normed space

... In this article, we study λ-double statistical convergence in a random -normed space which is a new and interesting idea. We show that some properties of λ-double statistical convergence of real numbers ...

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Quadratic Quartic Functional Equations in RN Spaces

Quadratic Quartic Functional Equations in RN Spaces

... In this sequel, we adopt the usual terminology, notations, and conventions of the theory of random normed spaces, as in 22, 23, 27–29. Throughout this paper, Δ is the space of distribution functions, ...

14

Nonlinear  Random Stability of an ACQ Functional Equation

Nonlinear Random Stability of an ACQ Functional Equation

... of random normed spaces RN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ...in ...

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Random Stability of an Additive Quadratic Quartic Functional Equation

Random Stability of an Additive Quadratic Quartic Functional Equation

... of random normed spaces RN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator ...in ...

18

Generalized Ulam Hyers Stability of Jensen Functional Equation in Šerstnev PN Spaces

Generalized Ulam Hyers Stability of Jensen Functional Equation in Šerstnev PN Spaces

... various spaces like fuzzy normed spaces, random normed spaces, quasi-Banach spaces, quasi-normed linear spaces, and Banach algebras by various authors like ...

14

Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces

Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces

... The theory of fuzzy sets was introduced by Zadeh in 1965 [31]. After the pioneer- ing work of Zadeh, there has been a great effort to obtain fuzzy analogues of classical theories. Among other fields, a progressive ...

12

On n normed spaces

On n normed spaces

... 4. Concluding remark. We have shown that an n-normed space with n ≥ 2 is an (n − 1)-normed space and that, for the standard or finite-dimensional case, the (n − 1)-norm can be derived from the n-norm in such ...

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