Iranian Journal of Mathematical Sciences and Informatics
Volume:19 Issue: 2, Nov 2024

By using the integral arithmetic mean and the Lah-Ribarič inequality we give the extension of Wulbert’s result from [15]. Also, we obtain inequalities with divided differences using the Lah-Ribarič inequality. As a consequence, the convexity of higher order for function defined by divided difference is proved. Further, we construct a new family of exponentially convex functions and Cauchy-type means by exploring at linear functionals with the obtained inequalities.

Let G be a group, R be a G-graded commutative ring with identity, M be a unitary graded R-module, Specg(R) be the set of graded prime ideals of R, and Cl.Specg(M) be the set of all graded classical prime submodules of M. In this paper among other things, the author studied the Zariski topology on both and Cl.Specg(M), and investigate some properties of the Zariski topology on Cl.Specg(M) and some conditions under which the graded classical prime spectrum of M is a spectral for its Zariski topology.

This paper focuses on the Γ–semihypergroups. Our goal seeks to find the conditions of sub–Γ–semihypergroup using bi–bases properties. We provide definitions and explain some properties of bi–bases in Γ– semihypergroups. The findings extend the results from bi–bases of Γ– semigroups. The findings demonstrate that if B is a bi–bases of a Γ– semihypergroup H; then, B is a sub–Γ–semihypergroup of H if and only if for any b, c ∈ B and γ ∈ Γ, b ∈ bγc or c ∈ bγc.

Argerami and Farenick have found conditions for the injective envelope of a separable C∗-algebra to be a von Neumann algebra. In this paper, we introduce an equivalent version of this result by finding conditions for the G-injective envelope of a separable G-C∗-algebra A to be a von Neumann algebra, when G is a discrete group acting on A.

In this paper, we define (ψ, ϕ)-Contraction Type T-coupling, establish a theorem satisfying such contraction condition, and prove the existence and uniqueness of coupled coincidence and coupled common fixed points in metric space. Here ψ and ϕ are two altering distance functions and T is a SCC-Map for metric spaces. Our results extend and generalize several related results in the existing literature. We also provided two examples to verify our main results.

The notion and some properties of (strongly) B-rings, in a natural way, are extended to (strongly) B- and (strongly) BJ-semirings which is somewhat similar to the notion of rings having stable range 2. Results are given showing the connection between several types of semirings whose finite sequences satisfy some stability condition, some involving the Jacobson k-radical of the semiring R. Besides some examples and other results, it is shown that R[x], the semiring of polynomials over a semiring R, is not a B-semiring (consequently, not a strongly B-semiring) when R is a zerosumfree semiring. We also study some algebraic properties of the S-relative B- and BJ-semirings with respect to a nonempty subset S of R.

In this paper, we introduce the notion of nonuniform semiorthogonal wavelet frame associated with nonuniform frame multiresolution analysis on non-Archimedean fields and provide their characterization by means of some basic equations in the frequency domain.

In this paper, we consider a population model with piecewise constant argument and show that every nonoscillatory solution approaches the equilibrium point as t tends to infinity. Moreover, we investigate every positive solution of the model that oscillates about the positive equilibrium point. Also, we give two examples to support the theorems.

In this paper, we discuss the inheritance of strict convexity, uniform convexity and local uniform convexity by the quotient spaces of metric linear spaces. We also show that, as in the case of normed linear spaces, completeness is a three- space property in metric linear spaces as well.

In the paper, we consider a type of Cattaneo equation with time fractional derivative without singular kernel based on fourth-order compact finite difference (CFD) in the space directions. In case of two dimensional, two alternating direction implicit (ADI) methods are proposed to split the equation into two separate one dimensional equations. The time fractional derivation is described in the Caputo-Fabrizio’s sense with scheme of order O(τ2). The solvability, unconditional stability and H1 norm convergence of the scheme are proved. Numerical results confirm the theoretical results and the effectiveness of the proposed scheme.

The method used in this research consists of a hybrid of the Block-Pulse functions and third-kind Chebyshev polynomials for solving systems of Fredholm integral differential equations. Through the use of an operational matrix representing the derivation, the problem is represented by a system of algebraic equations. Some examples are provided to illustrate the simplicity and effectiveness of the utilized method. In addition, results of the presented method have been compared with those obtained from the Tau method and variational iteration method that reveal the proposed scheme to be more applicable.

The affine general linear group 25:GL(5, 2) of GL(6, 2) has 6 conjugacy classes of maximal subgroups. The largest two maximal subgroups are of the forms 21+8:GL(4, 2) and 24+5:GL(4, 2). In this article we consider the group 24+5:GL(4, 2), which we denote by ${bar G}$. Firstly we determine its conjugacy classes using the coset analysis technique. The structures of the inertia factor groups are also determined. We then compute all the Fischer matrices and apply the Clifford-Fischer theory to compute the ordinary character table of ${bar G}$. Using information on conjugacy classes, Fischer matrices and both ordinary and projective character tables of the inertia factor groups, we concluded that we need to use the ordinary character tables of all the inertia factor groups to construct the character table of ${bar G}$. The character table of ${bar G}$ is a 75×75 complex valued matrix and we supply it (in the format of Clifford-Fischer theory) at the end of this paper as Table 6.

It is proved that if $sum_{gin G} a_g g$ is a non-zero zero divisor element of the complex group  algebra $mathbb{C}G$ of a torsion-free group G then  $2sum_{gin G} |a_g|^2<big( sum_{gin G} |a_g|big)^2$.

Let L be a Lie crossed module and Actpi(L) and Actz(L) be the pointwise inner actor and center actor of L, respectively. We will give a necessary and sufficient condition under which Actpi(L) and Actz(L) are equal.

In this research work, we introduce a generalization of the notion of kernel of a set in topological spaces endowed with an ideal, which is a fundamental tool to obtain new modifications of open sets and closed sets. Using this generalized kernel, we define and characterize new low separation axioms in other contexts obtained from a topological space endowed with an ideal. Also, we study the invariance of these low separation axioms under certain types of continuity defined in this novel theoretical framework.