scholarly journals Approximate Euler-Lagrange Quadratic Mappings in Fuzzy Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hark-Mahn Kim ◽  
Juri Lee
Keyword(s):  
Banach Spaces ◽  
Quadratic Mappings

scholarly journals Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
Hark-Mahn Kim
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
Linear Spaces ◽  
Quadratic Mappings

we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability inp-Banach spaces.

scholarly journals Approximate multi-Jensen and multi-quadratic mappings in 2-Banach spaces

2013 ◽  
Vol 29 (2) ◽  
pp. 159-166
Author(s):  
KRZYSZTOF CIEPLINSKI ◽  
◽  
TIAN ZHOU XU ◽  
Keyword(s):  
Banach Spaces ◽  
Ulam Stability ◽  
Quadratic Mappings ◽  
Additive Mappings

In this paper we prove the generalized Hyers-Ulam stability of multi-Jensen and multi-quadratic mappings in 2-Banach spaces. The corollaries from our main results correct some outcomes from [Park, W.-G., Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl., 376 (2011) 193–202].

scholarly journals Ulam Stability of a Functional Equation in Various Normed Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1119
Author(s):  
Krzysztof Ciepliński
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Functional Equations ◽  
Direct Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quadratic Mappings ◽  
The Stability

In this note, we study the Ulam stability of a general functional equation in four variables. Since its particular case is a known equation characterizing the so-called bi-quadratic mappings (i.e., mappings which are quadratic in each of their both arguments), we get in consequence its stability, too. We deal with the stability of the considered functional equations not only in classical Banach spaces, but also in 2-Banach and complete non-Archimedean normed spaces. To obtain our outcomes, the direct method is applied.

scholarly journals Approximate Multi-Jensen, Multi-Euler-Lagrange Additive and Quadratic Mappings in -Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Tian Zhou Xu
Keyword(s):  
Banach Spaces ◽  
Direct Method ◽  
Ulam Stability ◽  
Quadratic Mappings

We prove the generalized Hyers-Ulam stability of multi-Jensen, multi-Euler-Lagrange additive, and quadratic mappings in -Banach spaces, using the socalled direct method. The corollaries from our main results correct some outcomes from Park (2011).

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