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ISSN: 2582-0818

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Volume 7, Number 1 (2024)-Table of Contents

Open AccessArticle

e⋆-local Functions and Ψe⋆ -operator in Ideal Topological Spaces

Annals of Communications in Mathematics 2024

, 7 (1)

, 1-9

DOI: https://doi.org/10.62072/acm.2024.070101

AbstractThe main goal of this paper is to introduce another local function to give the possibility of obtaining a Kuratowski closure operator. On the other hand, e⋆-local functions defined for ideal topological spaces have not been found in the current literature. e⋆-local functions for the ideal topological spaces have been described within this work. Moreover, with the help of e⋆-local functions Kuratowski closure operators cl∗e⋆ I and τ ∗e⋆ topology are obtained. Many theorems in the literature have been revised according to the definition of e⋆-local functions
Open AccessArticle

On Interval Valued Fuzzy Prime Ideals of Γ−semirings

Annals of Communications in Mathematics 2024

, 7 (1)

, 10-20

DOI: https://doi.org/10.62072/acm.2024.070102

AbstractIn this paper, we introduce the notion of interval valued fuzzy prime ideals of Γ−semirings.We study, some properties of prime ideals of a Γ−semirng in terms of interval valued fuzzy ideals.
Open AccessArticle

Quasistatic Evolution of Damage in Thermo-electro-elastic-viscoplastic Materials With Normal Compliance

Annals of Communications in Mathematics 2024

, 7 (1)

, 21-41

DOI: https://doi.org/10.62072/acm.2024.070103

AbstractWe have studied contact problem in a quasistatic process with boundary conditions, for which we couple a thermal effect and damage and electrical effect. We assume that the contact is with normal compliance in a form with a gap function and is associated to a slip rate-dependent version of Coulomb’s law of dry friction. We give the variational formulation, then the existence and the uniqueness of the weak solution. The proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, and fixed points.
Open AccessArticle

Distributional Boundary Values of Analytic Functions

Annals of Communications in Mathematics 2024

, 7 (1)

, 42-46

DOI: https://doi.org/10.62072/acm.2024.070104

Abstract

Let D be a connected bounded domain in R2, S be its boundary which is closed, connected and smooth. Let Φ(z) = 1/2πi ∫S φ(s)ds/(s-z), φ ∈ X, z = x + iy, X is a Banach space of linear bounded functionals on Hμ, a Banach space of distributions, and Hμ is the Banach space of Hoelder-continuous functions on S with the usual norm. As X one can use also the space Hoelder continuous of bounded linear functionals on the Sobolev space H on S. Distributional boundary values of Φ(z) on S are studied in detail. The function Φ(t), t ∈ S, is defined in a new way. Necessary and sufficient conditions are given for φ ∈ X to be a boundary value of an analytic in D function. The Cauchy formula is generalized to the case when the boundary values of an analytic function in D are tempered distributions. The Sokhotsky-Plemelj formulas are derived for φ ∈ X.

Open AccessArticle

On Relative (2, 2)-Γ-hyperideals of 2-duo Ordered Γ-semihypergroups

Annals of Communications in Mathematics 2024

, 7 (1)

, 47-56

DOI: https://doi.org/10.62072/acm.2024.070105

AbstractIn this paper, first we obtain the necessary and sufficient condition for an ordered Γ-semihypergroup H to be a relative completely regular 2-duo ordered Γ-semihypergroup for any relative (2, 2)-Γ-hyperideal as well as for any relative (2, 2)-quasi-Γ-hyperideal of H. Then, we find the necessary and sufficient condition that Q = (Q2]S for every relative (2, 2)-Γ-hyperideal Q of H to be a relative quasi-Γ-prime with S ⊆ H. Finally, we prove the necessary and sufficient condition for relative (2, 2)-Γ-hyperideal to be a relative quasi-Γ-prime for a relative completely regular and relative (2, 2)-Γ-hyperideal of H making a chain with inclusive relation.
Open AccessArticle

Common Limit Range Property in Neutrosophic Menger Spaces

Annals of Communications in Mathematics 2024

, 7 (1)

, 57-70

DOI: https://doi.org/10.62072/acm.2024.070106

AbstractThe aim of this paper is to prove some common fixed-point theorems for weakly compatible mappings in Neutrosophic Menger Spaces satisfying common limit range property. Some examples are also given which demonstrate the validity of our results. As an application of our main result, we present a common fixed point theorems for four finite families of self-mappings in Menger spaces.
Open AccessArticle

Ordered Γ-semihypergroup of the Associated Γ-semihypergroup with All Relative Bi-Γ-hyperideals

Annals of Communications in Mathematics 2024

, 7 (1)

, 71-79

DOI: https://doi.org/10.62072/acm.2024.070107

AbstractIn this paper, the main goal is to study an ordered Γ-semihypergroup H in the context of the characterizations of the associated Γ-semihypergroup B(H) of all bi-Γ-hyperideals of H. We show that an ordered Γ-semihypergroup H is a Clifford ordered Γ-semihypergroup if and only if B(H) is a semilattice. We also show that a Γsemihypergroup B(H) is a normal band if and only if the ordered Γ-semihypergroup H is simultaneously regular and intra regular. Furthermore, for each subclass S with many bands, we prove that for an ordered Γ-semihypergroup H, the conditional inclusion B(H) ∈ S holds true.
Open AccessArticle

Some New Results on JU-algebras

Annals of Communications in Mathematics 2024

, 7 (1)

, 80-90

DOI: https://doi.org/10.62072/acm.2024.070108

AbstractJU-algebra (or weak KU-algebra) is a generalization of a KU-algebra. The concepts of atoms in JU-algebras are introduced and their important basic properties are registered. In addition to the previous one, an extension of a (weak) KU-algebra A to the JU-algebra A ∪ {w} was designed.