### Abstract

The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The aim of this paper is to give the definitions of F-invariant sets denoted by M in case of M ∊ X<sup>6</sup> in cone and ordered cone version. we also establish some tripled fioxed point theorems in cone metric spaces under the concept of an F-invariant set for mappings F : X<sup>3</sup> → X and c-distance on the one hand, and in partially ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric spaces,respectively. An interesting example is given to support our results.

Original language | English |
---|---|

Pages (from-to) | 750-762 |

Number of pages | 13 |

Journal | Journal of Nonlinear Science and Applications |

Volume | 8 |

Issue number | 5 |

Publication status | Published - 17 Jul 2015 |

### Fingerprint

### Keywords

- C-distance
- Cone metric spaces
- F-invariant set
- Partially ordered cone metric spaces
- Tripled fixed points

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis

### Cite this

*Journal of Nonlinear Science and Applications*,

*8*(5), 750-762.

**Tripled fixed point theorems in cone metric spaces under F-invariant set and c-distance.** / Abusalim, Sahar Mohammad; Md. Noorani, Mohd. Salmi.

Research output: Contribution to journal › Article

*Journal of Nonlinear Science and Applications*, vol. 8, no. 5, pp. 750-762.

}

TY - JOUR

T1 - Tripled fixed point theorems in cone metric spaces under F-invariant set and c-distance

AU - Abusalim, Sahar Mohammad

AU - Md. Noorani, Mohd. Salmi

PY - 2015/7/17

Y1 - 2015/7/17

N2 - The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The aim of this paper is to give the definitions of F-invariant sets denoted by M in case of M ∊ X6 in cone and ordered cone version. we also establish some tripled fioxed point theorems in cone metric spaces under the concept of an F-invariant set for mappings F : X3 → X and c-distance on the one hand, and in partially ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric spaces,respectively. An interesting example is given to support our results.

AB - The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The aim of this paper is to give the definitions of F-invariant sets denoted by M in case of M ∊ X6 in cone and ordered cone version. we also establish some tripled fioxed point theorems in cone metric spaces under the concept of an F-invariant set for mappings F : X3 → X and c-distance on the one hand, and in partially ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric spaces,respectively. An interesting example is given to support our results.

KW - C-distance

KW - Cone metric spaces

KW - F-invariant set

KW - Partially ordered cone metric spaces

KW - Tripled fixed points

UR - http://www.scopus.com/inward/record.url?scp=84937160348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937160348&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84937160348

VL - 8

SP - 750

EP - 762

JO - Journal of Nonlinear Science and Applications

JF - Journal of Nonlinear Science and Applications

SN - 2008-1898

IS - 5

ER -