# Ulam–Hyers Stability via Fixed Point Results for Special Contractions in b-Metric Spaces

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition 1**

**Example 1.**

**Example 2.**

- (1)
- The gap functional, i.e., the distance between a point $a\in M$ and a set $B\subset M$:$$D(a,B):=\mathrm{inf}\left\{d\right(a,b\left)\phantom{\rule{3.33333pt}{0ex}}\right|\phantom{\rule{3.33333pt}{0ex}}b\in B\};$$
- (2)
- The excess functional of A over B generated by d:$$e(A,B):=sup\left\{D\right(a,B\left)\phantom{\rule{3.33333pt}{0ex}}\right|\phantom{\rule{3.33333pt}{0ex}}a\in A\};$$
- (3)

**Lemma 1.**

**Definition 2**

**Remark 1.**

**Theorem 1.**

## 3. Fixed Point Results and Ulam–Hyers Stability

**Lemma 2**

**Theorem 2.**

**Proof.**

**Definition 3.**

**Theorem 3.**

**Proof.**

**Theorem 4.**

## 4. Strict Fixed Point Results

**Theorem 5.**

**Proof.**

**Lemma 3.**

**Theorem 6.**

**Proof.**

**Definition 4.**

**Theorem 7.**

**Proof.**

**Corollary 1.**

**Proof.**

**Remark 3.**

**Open Problem.**

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Bota, M.-F.; Micula, S.
Ulam–Hyers Stability via Fixed Point Results for Special Contractions in *b*-Metric Spaces. *Symmetry* **2022**, *14*, 2461.
https://doi.org/10.3390/sym14112461

**AMA Style**

Bota M-F, Micula S.
Ulam–Hyers Stability via Fixed Point Results for Special Contractions in *b*-Metric Spaces. *Symmetry*. 2022; 14(11):2461.
https://doi.org/10.3390/sym14112461

**Chicago/Turabian Style**

Bota, Monica-Felicia, and Sanda Micula.
2022. "Ulam–Hyers Stability via Fixed Point Results for Special Contractions in *b*-Metric Spaces" *Symmetry* 14, no. 11: 2461.
https://doi.org/10.3390/sym14112461