# Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II

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## Abstract

**:**

## 1. Introduction

Assume that ${G}_{1}$ is a group and ${G}_{2}$ is a metric group equipped with the metric $d(\xb7,\xb7)$. Given an arbitrary constant $\epsilon >0$, can we choose a constant $\delta >0$ such that for every function $h:{G}_{1}\to {G}_{2}$ satisfying $d\left(h\right(xy),h(x\left)h\right(y\left)\right)<\delta $ for all $x,y\in {G}_{1}$ there exists a group homomorphism $H:{G}_{1}\to {G}_{2}$ with $d\left(h\right(x),H(x\left)\right)<\epsilon $ for all $x\in {G}_{1}$?

**Theorem**

**1.**

## 2. Preliminaries

**Theorem**

**2.**

## 3. Generalized Hyers-Ulam Stability of (2)

**Theorem**

**3.**

**Proof.**

**Corollary**

**1.**

**Corollary**

**2.**

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Jung, S.-M.; Lee, K.-S.; Rassias, M.T.; Yang, S.-M.
Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II. *Mathematics* **2020**, *8*, 1299.
https://doi.org/10.3390/math8081299

**AMA Style**

Jung S-M, Lee K-S, Rassias MT, Yang S-M.
Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II. *Mathematics*. 2020; 8(8):1299.
https://doi.org/10.3390/math8081299

**Chicago/Turabian Style**

Jung, Soon-Mo, Ki-Suk Lee, Michael Th. Rassias, and Sung-Mo Yang.
2020. "Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II" *Mathematics* 8, no. 8: 1299.
https://doi.org/10.3390/math8081299