scholarly journals Generalized Hyers-Ulam Stability of the Pexiderized Cauchy Functional Equation in Non-Archimedean Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Abbas Najati ◽  
Yeol Je Cho
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Cauchy Functional Equation ◽  
Pexiderized Cauchy Functional Equation

scholarly journals On Pexider Differences in Topological Vector Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Abbas Najati ◽  
M. R. Abdollahpour ◽  
Gwang Hui Kim
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Rational Numbers ◽  
Vector Spaces ◽  
Cauchy Functional Equation ◽  
Topological Vector Spaces ◽  
Hausdorff Topological Vector Space ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Pexiderized Cauchy Functional Equation

Let be a normed space and a sequentially complete Hausdorff topological vector space over the field of rational numbers. Let and where . We prove that the Pexiderized Jensen functional equation is stable for functions defined on and taking values in . We consider also the Pexiderized Cauchy functional equation.

scholarly journals Ulam’s Type Stability and Generalized Norms

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 502
Author(s):  
Laura Manolescu
Keyword(s):  
Functional Equation ◽  
Symmetric Spaces ◽  
Ulam Stability ◽  
Cauchy Equation ◽  
Cauchy Functional Equation ◽  
Type V ◽  
Ulam’S Type Stability

A symmetric functional equation is one whose form is the same regardless of the order of the arguments. A remarkable example is the Cauchy functional equation: f ( x + y ) = f ( x ) + f ( y ) . Interesting results in the study of the rigidity of quasi-isometries for symmetric spaces were obtained by B. Kleiner and B. Leeb, using the Hyers-Ulam stability of a Cauchy equation. In this paper, some results on the Ulam’s type stability of the Cauchy functional equation are provided by extending the traditional norm estimations to ther measurements called generalized norm of convex type (v-norm) and generalized norm of subadditive type (s-norm).

scholarly journals On the Ulam Stability of Cauchy Functional Equation in IFN-Spaces

2014 ◽  
Vol 8 (3) ◽  
pp. 1135-1143 ◽  
Author(s):  
A. Alotaibi ◽  
M. Mursaleen ◽  
H. Dutta ◽  
S. A. Mohiuddine
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Cauchy Functional Equation

scholarly journals Stability of Functional Equations in Dislocated Quasi-Metric Spaces

2018 ◽  
Vol 32 (1) ◽  
pp. 215-225 ◽  
Author(s):  
Beata Hejmej
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Linear Functional ◽  
Metric Spaces ◽  
Linear Functional Equation ◽  
Ulam Stability ◽  
Cauchy Functional Equation ◽  
Complete Metric Spaces ◽  
Stability Of Functional Equations ◽  
Quasimetric Space

Abstract We present a result on the generalized Hyers-Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove stability of the Cauchy functional equation and the linear functional equation in two variables, also for functions taking values in a complete dislocated quasimetric space. In this way we generalize some earlier results proved for classical complete metric spaces.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

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