# Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in b-Metric Spaces

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

- (1)
- $\delta (u,v)=0$ if and only if $u=v$;
- (2)
- $\delta (u,v)=\delta (v,u)$ for all $u,v\in \mathsf{\Omega}$;
- (3)
- there exists a real number $s\ge 1$ such that $\delta (u,z)\le s\left[\delta \right(u,v)+\delta (v,z\left)\right]$ for all $u,v,z\in \mathsf{\Omega}$.

**Definition**

**2.**

**Theorem**

**1.**

**Lemma**

**1.**

**Remark**

**1.**

**Lemma**

**2.**

**Remark**

**2.**

## 3. Main Results

**Definition**

**3.**

**Theorem**

**2.**

**Proof.**

**Example**

**1.**

**Definition**

**4.**

**Theorem**

**3.**

**Proof.**

**Example**

**2.**

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Debnath, P.; de La Sen, M.
Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in *b*-Metric Spaces. *Mathematics* **2019**, *7*, 849.
https://doi.org/10.3390/math7090849

**AMA Style**

Debnath P, de La Sen M.
Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in *b*-Metric Spaces. *Mathematics*. 2019; 7(9):849.
https://doi.org/10.3390/math7090849

**Chicago/Turabian Style**

Debnath, Pradip, and Manuel de La Sen.
2019. "Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in *b*-Metric Spaces" *Mathematics* 7, no. 9: 849.
https://doi.org/10.3390/math7090849