Fixed and common fixed point results for cyclic mappings of Ω -distance

Shatanawi, Wasfı; Bataihah, Anwar; Pitea, Ariana

doi:10.22436/jnsa.009.03.02

Cited by 10 publications

(4 citation statements)

References 20 publications

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“…They continued their work to construct and prove some fixed and coupled fixed point theorems for a nonlinear contraction [25] . Other interesting results are gained by Shatanawi et al [23,24] in 2016. Shatanawi et al [24] have introduced new fixed point and common fixed point for mappings of the cyclic form of Ω-distance in G-metric space.…”

Section: Definition 14 ([14])mentioning

confidence: 85%

“…Other interesting results are gained by Shatanawi et al [23,24] in 2016. Shatanawi et al [24] have introduced new fixed point and common fixed point for mappings of the cyclic form of Ω-distance in G-metric space. Next, Shatanawi et al [23] improved the usability of this notion by introducing a new contraction mapping called Ω-suzuki-construction in g-metric space.…”

Section: Definition 14 ([14])mentioning

confidence: 85%

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Contraction mapping principle in partially ordered quasi metric space concerning to w-distances

Zuhra¹,

Noorani²,

Shaddad³

2017

J. Nonlinear Sci. Appl.

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The fixed point theorems in various contraction mappings have been provided by many researchers. Some of them used certain functions in mapping to guarantee the existence of fixed point. The purpose of this paper is to present some fixed point result on contraction mapping in partially ordered quasi-metric space that applying a w-distance. The generalized altering distance function on the mapping plays a role in theorems. The results extend some well-known results in the references. We also improve these new results to the common fixed point.

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Section: Definition 14 ([14])mentioning

confidence: 85%

Section: Definition 14 ([14])mentioning

confidence: 85%

Contraction mapping principle in partially ordered quasi metric space concerning to w-distances

Zuhra¹,

Noorani²,

Shaddad³

2017

J. Nonlinear Sci. Appl.

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“…The theorem of Banach asserts the existence and uniqueness of fixed point for any contraction mapping on a complete metric space. Then after, many researchers generalized the result of Banach in two directions; some of them by replacing the frame of distance space (for example see [2]- [16]), and the others by improving the contraction condition (for example see [17]- [30]). In this manuscript, we consider the following notations: W is a non empty set, R the set of all real numbers, N the set of all natural numbers and G the set of all fixed point for a self mapping g : W → W .…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

A new contraction based on ℋ-simulation functions in the frame of extended b-metric spaces and application

Qawasmeh

Hatamleh

2023

IJECE

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The conceptions of b-metric spaces and metric spaces play a remarkable role in proving many theorems of uniqueness and existence solution of such equations as integral or differential equations. The conception of extended b-metric spaces is considered as a generalization concept of b-metric spaces and metric spaces and this concept was employed to unify some new fixed point results in the literature. On the other hand, a new concept of simulation functions founded in 2020 in the name of ℋ-simulation functions and employed this class of functions to unify some fixed point results in the literature. The main objective of this manuscript, is to establish a new contraction namely, (γ, ϕ, θ) ℋ-contraction, this contraction based on the concepts of extended b-metric spaces and the class of functions (ℋ-simulation functions) and the class of functions Θ-functions and the class of functions Φ-functions, We utilize this new contraction to unify the uniqueness and existence of fixed point results in the literature. In addition, some illustrative examples and an interesting application were established to show the novelty of our work.

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“…The notion of -metric spaces was introduced by Mustafa and Sims [5] as a generalization of metric spaces. Thereafter, -metric spaces have been studied and applied to obtain different kinds of fixed point theorems, see [6][7][8][9][10][11][12]. Aghajani et al [13] introduced the notion of -metric spaces based on -metric spaces and -metric spaces introduced by Bakhtin in [14].…”

Section: Introductionmentioning

confidence: 99%