# Ulam Stability of a Functional Equation in Various Normed Spaces

## Abstract

**:**

## 1. Introduction

**Example**

**1.**

## 2. Results

#### 2.1. Stability in Banach Spaces

**Theorem**

**1.**

**Proof.**

#### 2.2. Stability in 2-Banach Spaces

**Remark**

**1.**

- (i)
- if $x\in X$ and$$\parallel x,y\parallel =0,\phantom{\rule{2.em}{0ex}}y\in X,$$
- (ii)
- if the sequence ${({x}_{k})}_{k\in \mathbb{N}}$ is convergent, then$$\underset{k\to \infty}{lim}\parallel {x}_{k},y\parallel =\parallel \underset{k\to \infty}{lim}{x}_{k},y\parallel ,\phantom{\rule{2.em}{0ex}}y\in X.$$

**Theorem**

**2.**

**Proof.**

#### 2.3. Stability in Complete Non-Archimedean Normed Spaces

**Theorem**

**3.**

**Proof.**

## 3. Discussion

**Corollary**

**1.**

**Corollary**

**2.**

## 4. Conclusions

## Funding

## Conflicts of Interest

## References

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Ciepliński, K.
Ulam Stability of a Functional Equation in Various Normed Spaces. *Symmetry* **2020**, *12*, 1119.
https://doi.org/10.3390/sym12071119

**AMA Style**

Ciepliński K.
Ulam Stability of a Functional Equation in Various Normed Spaces. *Symmetry*. 2020; 12(7):1119.
https://doi.org/10.3390/sym12071119

**Chicago/Turabian Style**

Ciepliński, Krzysztof.
2020. "Ulam Stability of a Functional Equation in Various Normed Spaces" *Symmetry* 12, no. 7: 1119.
https://doi.org/10.3390/sym12071119