RGNNA Publishing Group. Mathematical Analysis and its Contemporary Applications 2716-9898 4 4 2022 12 01 On various properties of module Lau product of algebras 1 12 693326 10.30495/maca.2022.1955532.1055 EN Prakash A. Dabhi Department of Mathematics, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad - 380026, Gujarat, India Yuvraj D. Pipaliya Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar- 388120, Gujarat, India Lecturer in Mathematics, General Department, Government Polytechnic, Junagadh- 362263, Gujarat, India Journal Article 2022 03 25 Let $\mathcal{A},$ $\mathcal{B},$ 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.pdf
RGNNA Publishing Group. Mathematical Analysis and its Contemporary Applications 2716-9898 4 4 2022 12 01 Anti complex fuzzy Lie subalgebras under $S$-norms 13 26 693796 10.30495/maca.2022.1952804.1049 EN Rasul Rasuli Department of Mathematics, Payame Noor University(PNU), P. O. Box 19395-4697, Tehran, Iran Journal Article 2022 02 16 The 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.pdf
RGNNA Publishing Group. Mathematical Analysis and its Contemporary Applications 2716-9898 4 4 2022 12 01 Quasi fixed points of contractions on semi cone metric spaces 27 37 693797 10.30495/maca.2022.1956857.1058 EN Gurusamy Siva Department of Mathematics, Alagappa University, Karaikudi-630 003, India Journal Article 2022 04 17 In 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.pdf
RGNNA Publishing Group. Mathematical Analysis and its Contemporary Applications 2716-9898 4 4 2022 12 01 A modified Taylor-series for solving a Fredholm integral equation of the second kind 39 48 693798 10.30495/maca.2022.1956497.1056 EN Majid Amirfakhrian Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran Seyyed Mahmood Mirzaei Department of Mathematics, Gonbad Kavoos Branch, Islamic Azad University, Gonbad Kavoos, Iran 0000-0002-6644-1840 Journal Article 2022 04 12 In 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.pdf
RGNNA Publishing Group. Mathematical Analysis and its Contemporary Applications 2716-9898 4 4 2022 12 01 Mathematical analysis of regenerative point graphical technique (RPGT ) 49 56 694425 10.30495/maca.2022.1964808.1062 EN Shakuntla Singla Department of Mathematics and Humanities, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala-133207, Haryana, India Pooja Dhawan Department of Mathematics and Humanities, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala-133207, Haryana, India Journal Article 2022 08 04 In 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.pdf
RGNNA Publishing Group. Mathematical Analysis and its Contemporary Applications 2716-9898 4 4 2022 12 01 Fixed point theorems for cyclic contractions on intuitionistic generalized fuzzy metric spaces 57 68 696802 10.30495/maca.2022.1961664.1060 EN Jeyaraman Mathuraiveeran PG and Research Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivagangai, Affiliated to Alagappa University, Karaikudi, Tamil Nadu, India https://orcid.org/0 Suganthi Mookiah Research Scholar, PG and Research Department of Mathematics, Raja Doraisingam Government Arts College, Sivagangai 630561, Affiliated to Alagappa University, Karaikudi, India Department of Mathematics, Government Arts College, Melur, India 0000000297521827 A. Ramachandran Research Scholar, Suvarna Karnataka Institute of Studies and Research Center, Tumkur 572102, Karnataka, India Journal Article 2022 06 22 In 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