Journal of Mathematical Extension
Volume:16 Issue: 11, Nov 2022

In this paper, we consider some kinds of semiregular frames of translates on the Hilbert space L 2 (R d ). More precisely, we investigate the frames of the form {TAkf}k∈Zd where A is a real invertible d × d matrix, f ∈ L 2 (R d ) and it is a frame for the closed subspace generated by {TAkf}k∈Zd .

One of the considerable strategies for the investigation of integro-differential equation is stability. The notion of this strategy shows us that we can rest assured of the numerical results obtained from the computer software. Since there are usually large errors in the numerical results of singular differential equations, this strategy will help us to be able to examine singular equations more easily with computer software. In this work, we study the stability of a multisingular fractional boundary value problem in the sense of Hyers-Ulam stability.We also present three examples and three figures to illustrate our main result.

This paper is devoted to discuss N−Legendre and N−slant curves in the unit tangent bundles of Minkowski surfaces. Unit tangent bundles are considered with a natural diagonal structure which generalizes the standard contact metric structure.

Let G be a locally compact group and H be a compact subgroup of G. The aim of this paper is to characterize some homological properties of L 1 (G/H), C0(G/H) and M(G/H) as left Banach L 1 (G)-modules such as flatness, injectivity and projectivity. Moreover, we study the projectivity of C0(G/H) and M(G/H) as Banach left L 1 (G/H)-modules and M(G)-modules.

Suppose that T is a bounded operator from a Hilbert space H into H. In this paper, for an injective cohyponormal or complex symmetric operator T, we find a necessary and sufficient condition for T to have the Hyers-Ulam stability. Moreover, when T is injective, we find necessary and sufficient conditions for T ∗T to have the Hyers-Ulam stability.

In this paper, we consider fuzzy optimization problems more general than all those that exist in the literature by using the concept of metric-based differentiability of fuzzy-valued functions. We get necessary optimality conditions based on fuzzy stationary point definition, and we prove these conditions are also sufficient under new fuzzy invexity notions. We illustrate these results with numerical examples.

The dual notion of a nil module and the square submodule of a module over a commutative ring are defined. Moreover, besides other results, some properties of these new concepts are investigated.

In this paper, R is a commutative ring with a non-zero identity and M is a unital R-module. We introduce the comaximal colon ideal graph C ∗ (R) and colon submodule graph C ∗ (M); and study the interplay between the graph-theoretic properties and the corresponding algebraic structures. C ∗ (R) is a simple connected supergraph of the comaximal ideal graph C(R) with diam(C ∗ (R)) ≤ 2. Moreover, we prove that if |V(C ∗ (R)| ≥ 3, then gr(C ∗ (R)) = 3. We prove that if |Max(R)| = n, then C ∗ (R) containing a complete n-partite subgraph. Also if M is a finitely generated multiplication module, then C ∗ (R) ∼= C ∗ (M). Moreover, for Z-module Zn which n is not a prime, C ∗ (Zn) ∼= Kd(n), where d(n) is the number of all divisors of the positive integer n other than 1 and n.

A common fixed point theorem for a pair of Hβ -Hausdorff multi-valued operators for β ∈ [0, 1] is proved in a b-metric space. Our result is a proper extension and new variants of many well known contraction conditions existing in literature. As an application of our main result, we have proved an existence result for a common solution of a pair of nonlinear Volterra type integral equations

In this paper, first Szabo operator related to the Ricci operator of Lorentzian 3-manifold in the algebraic setting is determined. Then, a necessary and sufficient condition for a Lorentzian 3-manifolds admitting a parallel line field with vanishing Szabo operator is obtained.