Regularities in Ordered n-Ary Semihypergroups

Daengsaen, Jukkrit; Leeratanavalee, Sorasak

doi:10.3390/math9161857

Mathematics

2021

DOI: 10.3390/math9161857

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Regularities in Ordered n-Ary Semihypergroups

Jukkrit Daengsaen

Sorasak Leeratanavalee

Abstract: This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1≤j≤n and n≥3. We first introduce the notion of (softly) left regularity, (softly) right regularity, (softly) intra-regularity, complete regularity, generalized regularity of ordered n-ary semihypergroups and investigate their related properties. Several characterizations of them in terms of j-hyperideals are provided. Finally, the relationships between var… Show more

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“…The well-known Bannack deflationary theorem uses the process of Picard's algorithm to approximate the fixed− point [1]. Some other well-known iterative processes are Agarwal [2], Noor [3], SP [4], Piccard S [5], and so on. Recently, Qing and Qhou [6] extended their results to a random period and the Ishikawa algorithm.…”

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Study Strong Convergence and Acceleration of New Iteration Type Three – Step

Maibed¹,

Al-Hameedwi²

2023

IHJPAS

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The aim of this article, we define new iterative methods called three-step type in which Jungck resolvent CR-iteration and resolvent Jungck SP-iteration are discussed and study rate convergence and strong convergence in Banach space to reach the fixed point which is differentially solve of nonlinear equations. The studies also expanded around it to find the best solution for nonlinear operator equations in addition to the varying inequalities in Hilbert spaces and Banach spaces, as well as the use of these iterative methods to approximate the difference between algorithms and their images, where we examined the necessary conditions that guarantee the unity and existence of the solid point. Finally, the results show that resolvent CR-iteration is faster than resolvent Jungck SP-iteration using Jungck resolvent estimation.

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Study Strong Convergence and Acceleration of New Iteration Type Three – Step

Maibed¹,

Al-Hameedwi²

2023

IHJPAS

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Semilattice strongly regular relations on ordered $ n $-ary semihypergroups

Daengsaen¹,

Leeratanavalee

2021

MATH

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<abstract>In this paper, we introduce the concept of $ j $-hyperfilters, for all positive integers $ 1\leq j \leq n $ and $ n \geq 2 $, on (ordered) $ n $-ary semihypergroups and establish the relationships between $ j $-hyperfilters and completely prime $ j $-hyperideals of (ordered) $ n $-ary semihypergroups. Moreover, we investigate the properties of the relation $ \mathcal{N} $, which is generated by the same principal hyperfilters, on (ordered) $ n $-ary semihypergroups. As we have known from [<xref ref-type="bibr" rid="b21">21</xref>] that the relation $ \mathcal{N} $ is the least semilattice congruence on semihypergroups, we illustrate by counterexample that the similar result is not necessarily true on $ n $-ary semihypergroups where $ n\geq 3 $. However, we provide a sufficient condition that makes the previous conclusion true on $ n $-ary semihypergroups and ordered $ n $-ary semihypergroups where $ n\geq 3 $. Finally, we study the decomposition of prime hyperideals and completely prime hyperideals by means of their $ \mathcal{N} $-classes. As an application of the results, a related problem posed by Tang and Davvaz in [<xref ref-type="bibr" rid="b31">31</xref>] is solved.</abstract>

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Regularities in Ordered n-Ary Semihypergroups

Cited by 2 publications

References 18 publications

Study Strong Convergence and Acceleration of New Iteration Type Three – Step

Study Strong Convergence and Acceleration of New Iteration Type Three – Step

Semilattice strongly regular relations on ordered $ n $-ary semihypergroups

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