Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16126220250801Spaceability of the set of surjective bounded operators on Banach function spaces10711322494210.30504/jims.2025.512613.1250ENA. R.Bagheri SalecDepartment of Mathematics, University of Qom, P.O. Box 37161, Qom, Iran.0000-0002-4917-6125S. M.TabatabaieDepartment of Mathematics, University of Qom, P.O. Box 37161, Qom, Iran.A. M.JuweedDepartment of Mathematics, University of Qom, P.O. Box 37161, Qom, Iran.Journal Article20250315In this work, we prove that the set of all surjective bounded linear operators on a Banach function space in the context of a class of general sets, is spaceable. The obtained results not only prepare some new applications, but also improve the previous versions given for standard Banach sequence spaces.https://jims.ims.ir/article_224942_0e79fe4591937f52adcae7e02c1df13c.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16126220250801Theta method to approximate fixed points of nonexpansive multimaps in Banach spaces11513222843110.30504/jims.2025.468166.1195ENM.MeddahiLaboratory of Mathematical Analysis and Applications, Faculty of
Technology, University
of Hassiba Benbouali, Chlef, Algeria.0000-0001-6664-1087K.NachiLaboratory of Mathematical Analysis and Applications, University Oran 1,
Ahmed Ben Bella, El M'naoeur, BP 1524, Oran, Algeria.Journal Article20240716In this paper, we introduce a novel iterative scheme that integrates the Mann iteration process with the implicit $\theta$-method to approximate fixed points of nonexpansive multivalued mappings in Banach spaces. Under suitable assumptions, we establish both weak and strong convergence results for the proposed algorithm. Furthermore, we demonstrate the applicability of our method to variational inclusion problems and convex optimization problems. A numerical example is presented to illustrate the efficiency and effectiveness of the approach.https://jims.ims.ir/article_228431_ce8e1e807d910a1d827b008fc52b35c6.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16126220250801Fair coalition in graphs13314723134010.30504/jims.2025.538329.1273ENSaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, Yazd, Iran.0000-0002-1801-203XAbbasJafariDepartment of Mathematical Sciences, Yazd University, Yazd, Iran.MaryamSafazadehDepartment of Mathematical Sciences, Yazd University, Yazd, Iran.Journal Article20250731Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. For $k \geq 1$, a $k$-fair dominating set ($kFD$-set) in $G$, is a dominating set $S$ such that $|N(v) \cap D|=k$ for every vertex $ v \in V\setminus D$. A fair dominating set in $G$ is a $kFD$-set for some integer $k\geq 1$. We consider $1FD$-sets and define a fair coalition in a graph $G$ as a pair of disjoint subsets $A_1, A_2 \subseteq A$ that satisfy the following conditions: (a) neither $A_1$ nor $A_2$ constitutes a $1$-fair dominating set of $G$, and (b) $A_1\cup A_2$ constitutes a $1$-fair dominating set of $G$. A fair coalition partition of a graph $G$ is a partition $\Upsilon = \{A_1,A_2,\ldots,A_k\}$ of its vertex set such that every set $A_i$ of $\Upsilon$ is either a singleton $1$-fair dominating set of $G$, or is not a $1$-fair dominating set of $G$ but forms a fair coalition with another non-$1$-fair dominating set $A_j\in \Upsilon$. We define the fair coalition number of $G$ as the maximum cardinality of a fair coalition partition of $G$, and we denote it by $\mathcal{C}_f(G)$. We initiate the study of the fair coalition in graphs and obtain $\mathcal{C}_f(G)$ for some specific graphs.https://jims.ims.ir/article_231340_cb842e58996c8ee460326a4065182484.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16126220250801Adjacency spectrum and energy of the exact zero-divisor graph of $\mathbb{Z}_n$14915823317810.30504/jims.2025.546348.1284ENS. K.BabariyaDepartment of Mathematics, Dr. Subhash University, P.O. Box 362001, Junagadh, India.P. T.LalchandaniDepartment of Mathematics, Dr. Subhash University, P.O. Box 362001, Junagadh, India.Journal Article20250910This paper investigates the exact zero-divisor graph $E\Gamma(R)$ of a commutative ring, with particular focus on $R=\mathbb{Z}_n$. We describe a partition of the vertex set of $E\Gamma(\mathbb{Z}_n)$ based on the greatest common divisors with $n$, which provides structural information about its components. The adjacency spectra and energies of $E\Gamma(\mathbb{Z}_{p^{2m+1}})$ and $E\Gamma(\mathbb{Z}_{p^{2m}})$ are computed explicitly, and their asymptotic behaviors are compared. The results reveal clear structural differences between the odd and even power cases.https://jims.ims.ir/article_233178_46a8603517fc211daa67fdfce0d94897.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16126220250801A study of $3$-derivations and their algebraic implications15917223295910.30504/jims.2025.520461.1257ENS.NazarlouDepartment of Mathematics, Azarbaijan Shahid Madani University, P.O. Box 53751, Tabriz, Iran.M. H.SattariDepartment of Mathematics, Azarbaijan Shahid Madani University, P.O. Box 53751, Tabriz, Iran.Journal Article20250504<span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman';">This paper explores the concept of<span lang="FA"> </span>$3$-derivations, <span lang="FA"></span>in the context of algebras<span lang="FA"></span>. <span lang="FA"></span>Building on prior work that established the invariance of primitive ideals<span lang="FA"></span>, <span lang="FA"></span>prime ideals<span lang="FA"></span>, <span lang="FA"></span>and minimal prime ideals under derivations<span lang="FA"></span>, <span lang="FA"></span>we extend these results to the case of<span lang="FA"> </span>$3$-derivations<span lang="FA"></span>. In particular<span lang="FA"></span>, <span lang="FA"></span>we show that several properties of primitive and prime ideals<span lang="FA"></span>, <span lang="FA"></span>previously proven for derivations<span lang="FA"></span>, <span lang="FA"></span>also hold in the setting of $3$-derivations<span lang="FA"></span>. Furthermore<span lang="FA"></span>, <span lang="FA"></span>we examine </span><span lang="FA" style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman';"></span><span style="mso-fareast-font-family: 'Times New Roman'; mso-bidi-font-family: 'Times New Roman';">$3$-derivations<span lang="FA"> </span>on triangular Banach algebras and show that a linear map<span lang="FA"> </span>$\mathcal{D}:\mathcal{T}\rightarrow\mathcal{T}$<span lang="FA"> </span>qualifies as a<span lang="FA"> </span>$3$-derivation if satisfies certain structural conditions.</span>https://jims.ims.ir/article_232959_7f52e16ee25c0fc14a08c42a79b103a6.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16126220250801On deferred statistical convergence in $\mathscr{A}$- metric spaces17318323488810.30504/jims.2025.540372.1276ENR.SunarMinistry of National Education, Afyonkarahisar, Turkiye.Journal Article20250812In this study, we introduce the notions of deferred statistical convergence and deferred strong Cesàro summability in $\mathscr{A}$-metric spaces, which represent some of the most prominent examples of generalized metric spaces that have been extensively investigated in recent developments in functional analysis and summability theory. Then, we conduct a detailed investigation into the relationships among statistical convergence, deferred statistical convergence, and deferred strong Cesàro summability in the context of $\mathscr{A}$-metric spaces. Additionally, we present several inclusion relations among these concepts within the context of $\mathscr{A}$-metric spaces.https://jims.ims.ir/article_234888_b9199aaeae3b668f1c338b5dae03b140.pdf