On ℋ-Simulation Functions and Fixed Point Results in the Setting of ωt-Distance Mappings with Application on Matrix Equations

Bataihah, Anwar; Shatanawi, Wasfı; Qawasmeh, Tariq; Hatamleh, Raéd

doi:10.3390/math8050837

Cited by 3 publications

(9 citation statements)

References 20 publications

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“…A triangular norm [10,33] 1] satisfying the following properties: associativity, commutativity, non-decreasing on each argument, and has one as unity (that is, t * 1 = t for all t ∈ [0, 1]). Usually, authors only consider continuous t-norms.…”

Section: Fuzzy Metric Spacesmentioning

confidence: 99%

“…Fixed-point theory is currently one of the most active fields in the area of nonlinear analysis and even in mathematics in general. Its results can be applied to an extensive set of distinct types of equations (integral, differential, matricial [1], etc.) in order to prove the existence and uniqueness of several classes of nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

“…we check that, under (Þ 2 ), Condition (Þ 4 ) implies Property (Þ 4 ). Let t ∈ (0, 1] be such that ϕ(t) ≥ η (1). To prove that t = 1, suppose, by contradiction, that t < 1.…”

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confidence: 99%

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Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

et al. 2021

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Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces.

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Section: Fuzzy Metric Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

et al. 2021

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“…Pioneer mathematicians, namely Khojasteh et al [32] established the notion of simulation functions in 2017 and they used them to unify many fixed point results in the literature. And then, many others mathematicians established other types of simulation functions such as Cho [33] established L -simulation functions and Bataihah et al [34] established the notion of H -simulation functions. Definition 4 [34]:…”

Section: Introduction and Mathematical Preliminariesmentioning

confidence: 99%

“…And then, many others mathematicians established other types of simulation functions such as Cho [33] established L -simulation functions and Bataihah et al [34] established the notion of H -simulation functions. Definition 4 [34]:…”

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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(H, Ωb)-Interpolative Contractions in Ωb-distance Mappings with Application

Qawasmeh

2023

Eur. J. Pure Appl. Math.

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Interpolative Kannan contractions are a refinement of Kannan contraction, which is considered as one of the significant notions in fixed point theory. Gb-metric spaces is considered as a generalized concept of both concepts b-metric and G-metric spaces therefore, the significant fixed and common fixed point results of the contraction based on this concept is generalized resultsfor both concepts. The purpose of this manuscript, is to take advantage to interpolative Kannan contraction together with the notion of Ωb which equipped with Gb-metric spaces and H simulation functions to formulate two new interpolative contractions namely, (H, Ωb)-interpolative contraction for self mapping f and generalized (H, Ωb)-interpolative contraction for pair of self mappings (f1, f2). We discuss new fixed and common fixed point theorems. Moreover, to demonstrate the applicability and novelty of our theorems, we formulate numerical examples and applications to illustrate the importance of fixed point theory in applied mathematics and other sciences.

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On ℋ-Simulation Functions and Fixed Point Results in the Setting of ωt-Distance Mappings with Application on Matrix Equations

Cited by 3 publications

References 20 publications

Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

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

(H, Ωb)-Interpolative Contractions in Ωb-distance Mappings with Application

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