Caspian Journal of Mathematical Sciences
Volume:12 Issue: 1, Winter Spring 2023

In this paper we consider the notion of quasi-multipliers on anℓ−algebra. We prove that, for a Banach ℓ−algebra A with an ultra approximateidentity, the set ℓQM(A) of all order continuous ℓ−quasi-multipliers on A is aBanach f−algebra. Further, we establish the relationship between the spaceℓQM(A) and the space ℓM(A) of all ℓ−multipliers on A. It is shown that, forcertain Banach ℓ−algebra A, there exists a map φ : ℓM(A) → ℓQM(A) whichis a positive, isometric and an algebraic lattice isomorphism.

In this paper, we solve a linear system of second-order boundary value problems by usingthe quadratic B-spline finite element method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analytical solution and some recent results.The obtained numerical results show that the method is efficient.

Kinematics studies the motion of a rigid object, such as displacement, velocity, acceleration, etc. A general planar motion can be defined as a combination of translation and rotation. Planar motion is widely used in many fields. Since most mobile robots move on flat terrain, many grippers and kinematic linkages use planar motion. The dual quaternion is the generalization of the quaternion and is used in various fields. In this paper, we introduce a new approach to planar motions by using the dual quaternion to study the pole points and pole trajectories, the triple coordinate system and the canonical system, and find the Euler-Savary equation.

In this paper, by utilizing the Sine-Gordan expansion method, soliton solutions of the higher-order improved Boussinesq equation, Kuramoto-Sivashinsky equation, and seventh-order Sawada-Kotera equation are obtained. Given partial differential equations are reduced to ordinary differential equations, by choosing the compatible wave transformation associated with the structure of the equation. Based on the solution of the Sine-Gordan equation, a polynomial system of equations is obtained according to the principle of homogeneous balancing. The solution of the outgoing system gives the parameters which are included by the solution. Plot3d and Plot2d graphics are given in detail. As a result, many different graphic models are obtained from soliton solutions of equations that play a very important role in mathematical physics and engineering.

In a given compact subset of R2 which is not necessarily convex, we study a pursuit differential game of many pursuers and one evader. The game must be done in this set. The constraints that we used for controls are coordinate-wise integral. Pursuers want to complete the pursuit and the evader is doing theopposite. Completion of the pursuit means that the distance of evader becomes zero with some pursuers. Some conditions for the completion of pursuit are derived.

In this paper, we study convergence analysis of the sequence generated by extragradient method for an infinite family of the equilibrium problems in Banach spaces. We first prove weak convergence of the generated sequence to a common solution of the infinite family of the equilibrium problems. Then we use Halpern type regularization method in order to prove strong convergence of the generated sequence to a common equilibrium point.

Assume that $A$ and $B$ areunital $C^{*}$-algebras and $\varphi:A\rightarrow B$ is a unitalpositive linear map. We show that if $B$ is commutative, then forall $x,y \in A$ and $\alpha, \beta \in \mathbb{C}$\begin{align*}|\varphi(xy)-\varphi(x)\varphi(y)| \leq & \left[\varphi(|x^{*}-\alpha 1_{A}|^{2})\right]^{\frac{1}{2}}\left[\varphi(|y-\beta1_{A}|^{2})\right]^{\frac{1}{2}} \\ & - |\varphi(x^{*}-\alpha 1_{A})||\varphi(y-\beta1_{A})|.\end{align*}Furthermore, we prove that if $z\in A$with $|z| =1$ and $\lambda, \mu \in \mathbb{C}$ are such that$Re(\varphi((x^{*}-\bar{\beta}z^{*})(\alpha z-x)))\geq 0$ and$Re(\varphi((y^{*}-\bar{\mu}z^{*})(\lambda z-y)))\geq 0$, then\begin{center}$|\varphi(x^{*}y)-\varphi(x^{*}z)\varphi(z^{*}y)| \leq \frac{1}{4}| \beta-\alpha | | \mu-\alpha | -$ \\$ \left[ Re(\varphi((x^{*}-\bar{\beta}z^{*})(\alpha z-x)))\right]^{\frac{1}{2}}\left[ Re(\varphi((y^{*}-\bar{\mu}z^{*})(\lambdaz-y)))\right] ^{\frac{1}{2}}.$\end{center}The presented bounds for the Gr\"{u}ss type inequalities on $C^{*}$-algebras improve the other ones in the literature under mild conditions. As an application, using our results, we give some inequalities in $L^{\infty}(\left[a,b\right])$, which refine the other ones in the literature.

In this paper, we prove a new integral identity, and then we establish some new Ostrowski's inequalities for fonctions whose first derivatives are harmonically quasi-convex via Riemann-Liouville fractional integrals.

This paper advances a new application of q-homotopy analysis method (q-HAM)to solve non-linear optimal control problems(NOCPs). First, the NOCP was transformedinto a non-linear two-point boundary value problem by using the Pontryaginsmaximum principle (PMP). Then, we applied the q-HAM to solve this system. Theproposed method is based on the HAM but the q-HAM, has an increased intervalof convergence than the HAM. Three examples are provided to demonstrate the reliabilityand efficiency of the method. Next, the numerical results of the proposedmethod are compared with those of other methods. As can be seen from the tables,the maximum error in the second and third examples is much better than othermethods.

In this paper, we extend and improve a common fixed point theorem of G. Jungck. We utilize the notions of weakly commuting and compatible mappings in probabilistic Banach spaces to prove some common fixed point theorems for improved type Jungck contractions.In addition, we present some examples which support our theorems.

The purpose of this article is to study the symmetries of the pseudo-Riemannian manifold $\mathbb{H}^{2}\times\mathbb{R}$. Specially, we study the existence of Ricci and matter collineations in this space.

If a clique and a regular graph are joined together the resulting graph is called a multicone graph. A graph $G$ is said to be determined by the spectrum of its signless Laplacian matrix (DQS, for short) if every graph with the same Laplacian spectrum is isomorphic to $G$. It is proved that all the multicone graphs $K_r\bigtriangledown sK_t$, except for $K_r\bigtriangledown 3K_1$, are DQS, where $K_r$ denots a complete graph with $r\geq 1$ vertices. Consequently, by using these results we give a response to an open problem in [24].

We investigate 2-dimensional viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions of similarities related to subalgebras are classified.In the end by using Bluman-Anco homotopy formula, we find local conservation laws of the viscoelastic equation.

In this paper we introduce the concept of rough I-statistical φ-convergence of real numbers as a generalization of rough statistical convergence as well as I-statistical φ-convergence. We study some of its fundamental properties. We obtain some results for rough I-statistical φ-convergence by introducing the rough I-statistical-φ limit set. So our main objective is to find out the different behaviour of the new convergence concept based on rough I-statistical-φ limit set.

In this article, we obtain new inequalities for Berezin radius. We have some improvements and interpolations of Berezin radius inequalities via operator convex function. These results offer several general forms and refinements of some known inequalities in the literature.

In this paper, we study the concept of $2_{\otimes}$-auto Engel groups. Among other results, we prove that for any group $G$, if every element of $G\otimes Aut(G)$ is $2_{\otimes}$-Engel group, then $\left<(g\otimes\alpha),(g\otimes\alpha)^{g^{\prime}\otimes\alpha^{\prime}}\right>$ is a nilpotent subgroup of class at most $2$ in $G\otimes Aut(G)$, for all $g,g^{\prime} \in G$ and $\alpha ,\alpha^{\prime}\in Aut(G)$.