RGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98984420221201On various properties of module Lau product of algebras11269332610.30495/maca.2022.1955532.1055ENPrakash A.DabhiDepartment of Mathematics, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad - 380026, Gujarat, IndiaYuvraj D.PipaliyaDepartment of Mathematics, Sardar Patel University, Vallabh Vidyanagar- 388120, Gujarat, IndiaLecturer in Mathematics, General Department, Government Polytechnic, Junagadh- 362263, Gujarat, IndiaJournal Article20220325Let $\mathcal{A},$ $\mathcal{B},$ and $\mathcal{X}$ be complex algebras, $\theta : \mathcal{B} \longrightarrow \mathcal{X}$ be an algebra homomorphism, and let $\mathcal{A}$ be an $\mathcal{X}$-bimodule. We define a product on $\mathcal{A} \times \mathcal{B}$ as $(a_1, b_1)(a_2,b_2) = (a_1 a_2 + a_1 \cdot \theta(b_2) + \theta(b_1) \circ a_2,b_1 b_2)$ for all $(a_1, b_1), (a_2,b_2) \in \mathcal{A} \times \mathcal{B}$ and write $\mathcal{A} \times \mathcal{B}$ with this product by $\mathcal{A} \times_\theta\mathcal{B}$. We shall study some basic properties of $\mathcal{A} \times_\theta \mathcal{B}$. When $\mathcal{A}$, $\mathcal{B}$ and $\mathcal{X}$ are Banach algebras, $\mathcal{A}$ is a Banach $\mathcal{X}$-bimodule, and $\theta$ is a continuous homomorphism with the norm at most $1$, we determine the ideals of $\mathcal{A} \times_\theta \mathcal{B}$ of a certain type, the Gelfand space of this Banach algebra, and the module multipliers of this Banach algebra.https://www.macajournal.com/article_693326_808320c02a44064cf83c9de9a6677a76.pdfRGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98984420221201Anti complex fuzzy Lie subalgebras under $S$-norms132669379610.30495/maca.2022.1952804.1049ENRasulRasuliDepartment of Mathematics, Payame Noor University(PNU), P. O. Box 19395-4697, Tehran, IranJournal Article20220216The objectives of this article are to present the notions of anti complex fuzzy subalgebras and anti complex fuzzy ideals of Lie algebras under $S$-norms and we prove that the level subset of them are also subalgebras and ideals of Lie algebras, respectively. Next, we introduce the union and summation of them and we prove that the union and summation of them are also anti complex fuzzy subalgebras and anti complex fuzzy ideals of Lie algebras under $S$-norms, respectively. Finally, we investigate the homomorphic image (pre-image) of them under Lie homomorphisms.https://www.macajournal.com/article_693796_ecce788d47ee8c528b5e761d640f750f.pdfRGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98984420221201Quasi fixed points of contractions on semi cone metric spaces273769379710.30495/maca.2022.1956857.1058ENGurusamySivaDepartment of Mathematics, Alagappa University, Karaikudi-630 003, IndiaJournal Article20220417In this article, the concept of semi-metric spaces is extended to semi-cone metric spaces. Also, some theorems for quasi-fixed points of Banach contractions, Kannan's contractions, and Chatterjea's contractions on semi-cone metric spaces are proved. Moreover, some quasi-fixed point results for different types of contraction mappings on semi-cone metric spaces are derived.https://www.macajournal.com/article_693797_ed14ca7efbd040f859e583663d0f3e72.pdfRGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98984420221201A modified Taylor-series for solving a Fredholm integral equation of the second kind394869379810.30495/maca.2022.1956497.1056ENMajidAmirfakhrianDepartment of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, IranSeyyed MahmoodMirzaeiDepartment of Mathematics, Gonbad Kavoos Branch, Islamic Azad University, Gonbad Kavoos, Iran0000-0002-6644-1840Journal Article20220412In this paper, we propose a Taylor series expansion method for the second kind of Fredholm integral equation with smooth kernels. This method converts the integral equation into a linear equation system to reduce the amount of computation. We present convergence conditions. Finally, we show the efficiency of the method using some numerical examples.https://www.macajournal.com/article_693798_ea525df7c7e48b4b1ae522b986c6cac4.pdfRGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98984420221201Mathematical analysis of regenerative point graphical technique (RPGT )495669442510.30495/maca.2022.1964808.1062ENShakuntlaSinglaDepartment of Mathematics and Humanities, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala-133207, Haryana, IndiaPoojaDhawanDepartment of Mathematics and Humanities, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala-133207, Haryana, IndiaJournal Article20220804In this paper, the behavioural analysis of a single-unit subdivision after a complete failure using the Regenerative Point Graphical Technique (RPGT) is discussed. Initially, the unit is fully operational which may have two types of malfunction, one is direct and the second is the partial failure mode. There is one server (fixer) that checks and fixes the unit for each failure. Incomplete failure of the unit cannot be restored to its original capacity. Each repair unit is subject to vandalism if the server reports that the unit cannot be repaired and replaced, following a normal distribution. The vague concept is used to determine unit failure/performance. Considering the levels of failure to be exponential, adjustment values are common and taking into account various possibilities, the system transformation diagram is developed to determine Primary, Second Circuits & Higher Education Foundations and Basic Status. The problem is constructed and resolved using RPGT to determine system parameters. System behaviour is discussed with the help of graphs.https://www.macajournal.com/article_694425_282b076ed4b99b6d64119e2596abfecc.pdfRGNNA Publishing Group.Mathematical Analysis and its Contemporary Applications2716-98984420221201Fixed point theorems for cyclic contractions on intuitionistic generalized fuzzy metric spaces576869680210.30495/maca.2022.1961664.1060ENJeyaramanMathuraiveeranPG and Research Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivagangai, Affiliated to Alagappa University, Karaikudi, Tamil Nadu, Indiahttps://orcid.org/0SuganthiMookiahResearch Scholar, PG and Research Department of Mathematics, Raja Doraisingam Government Arts College, Sivagangai 630561, Affiliated to Alagappa University, Karaikudi, IndiaDepartment of Mathematics, Government Arts College, Melur, India0000000297521827A.RamachandranResearch Scholar, Suvarna Karnataka Institute of Studies and Research Center, Tumkur 572102, Karnataka, IndiaJournal Article20220622In this work, we have brought in the notion of cyclic contraction into the intuitionistic generalized fuzzy metric spaces. We have set up some common fixed point theorems for these contractions and continuous mappings by considering their weakly commuting nature.https://www.macajournal.com/article_696802_d9785bf246bd488cbbb24813c09f6923.pdf