# Relatively Cyclic and Noncyclic P-Contractions in Locally K-Convex Space

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## Abstract

**:**

## 1. Introduction

- (i)
- $p\left(\lambda x\right)=\left|\lambda \right|p\left(x\right)$, $x\in X$ and $\lambda \in \mathbb{K}$.
- (ii)
- $p\left(x+y\right)\le max\left\{p\left(x\right),p\left(y\right)\right\}$, $x,y\in X$

## 2. Fixed Point Results for Relatively Cyclic P-Contractions

**Definition**

**1.**

**Theorem**

**1.**

**Proof.**

**Corollary**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Corollary**

**2.**

**Proof.**

## 3. Fixed Points of Relatively Noncyclic Mappings

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Lemma**

**1.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

- (i)
- ${T}_{|A}$ is p-contraction,
- (ii)
- T is relatively p-nonexpansive.

**Proof.**

## Author Contributions

## Funding

## Conflicts of Interest

## References

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## Share and Cite

**MDPI and ACS Style**

Mohamed, E.; Mohamed, A.; Samih, L.
Relatively Cyclic and Noncyclic *P*-Contractions in Locally K-Convex Space. *Axioms* **2019**, *8*, 96.
https://doi.org/10.3390/axioms8030096

**AMA Style**

Mohamed E, Mohamed A, Samih L.
Relatively Cyclic and Noncyclic *P*-Contractions in Locally K-Convex Space. *Axioms*. 2019; 8(3):96.
https://doi.org/10.3390/axioms8030096

**Chicago/Turabian Style**

Mohamed, Edraoui, Aamri Mohamed, and Lazaiz Samih.
2019. "Relatively Cyclic and Noncyclic *P*-Contractions in Locally K-Convex Space" *Axioms* 8, no. 3: 96.
https://doi.org/10.3390/axioms8030096