فهرست مطالب
 Volume:3 Issue: 2, 2022
 تاریخ انتشار: 1401/09/10
 تعداد عناوین: 12

Pages 16
Let X be a separable Banach space and M be a subspace of X. A bounded Linear operator T on X is subspace balanced convexcyclic for a subspace M, if there exists a vector x∈X such that the intersection of balanced convex hull of orb(T,x) with M is dense in M. We give an example of subspace balanced convexcyclic operator that is not balanced convexcyclic. Also we give an improvement of the Kitailike criterion for subspace balanced convexcyclicity and bring on with the HahnBanach characterization for subspace balanced convexcyclicity.
Keywords: Balanced convexcyclic operators, Kitai criterion, Hahn Banach theorem 
Pages 716
In the current paper, we study an inverse problem of identifying a timedependent forcing term in the onedimensional wave equation. We have the information of the wave displacement at two different instants of time and two sensor locations of space along with a dynamic type boundary condition. We prove the unique solvibility of the problem under some regularity and consistency conditions. Then, an approximate solution of the given inverse problem based upon deploying the Ritz technique along with the the collocation method is presented which converts the problem to a linear system of algebraic equations. The method takes advantage of the Tikhonov regularization technique to solve the linear system of equations that is not wellconditioned in order to achieve stable solutions. Numerical findings are also included to support the claim that the presented method is reliable in finding accurate and stable solutions.
Keywords: Inverse source problems, dynamictype boundary condition, collocation method, Tikhonov Regularization 
Pages 1724
In this paper we give a topologydynamical interpretation for the space of all integer sequences $P_n$ whose consecutive difference $P_{n+1}P_n$ is a bounded sequence. We also introduce a new concept textit{"Rigid Banach space"}. A rigid Banach space is a Banach space $X$ such that for every continuous linear injection $j:Xto X,;overline{J(X)}$ is either isomorphic to $X$ or it does not contain any isometric copy of $X$. We prove that $ell_{infty}$ is not a rigid Banach space. We also discuss about rigidity of Banach algebras.
Keywords: Rigid Banach space, sequence space, Primes 
Pages 2534
In this paper, we study the conformal transformation of some important and effective nonRiemannian curvatures in Finsler Geometry. We find the necessary and sufficient condition under which the conformal transformation preserves the Berwald curvature B, mean Berwald curvature E, Landsberg curvature L, mean Landsberg curvature J, and the nonRiemannian curvature H.
Keywords: Berwald curvature, mean Berwald curvature, Landsberg curvature, mean Landsberg curvature, the quantity H 
Pages 3558
In this paper, we deal with the existence and multiplicity solutions, for the following fractional discrete boundaryvalue problem { T +1∇α k (k∇α 0 (u(k))) + k∇α 0 (T +1∇α k (u(k))) = λf(k, u(k)), k ∈ [1, T]N0 , u(0) = u(T + 1) = 0, where 0 ≤ α ≤ 1 and 0∇α k is the left nabla discrete fractional difference and k∇α T +1 is the right nabla discrete fractional difference and f : [1, T]N0 × R → R is a continuous function and λ > 0 is a parameter. The technical approach is based on the critical point theory and some local minimum theorems for differentiable functionals. Several examples are included to illustrate the main results.
Keywords: Discrete fractional calculus, Discrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory 
Pages 5967
The main goal of this paper is to discuss the Callebaut inequality and meanconvex inequality from positive definite matrices to sector matrices in a more general setting. Afterward, several inequalities involved positive linear map, are presented for sector matrices. For instance, we show that if $ A,Bin {{mathcal S}_{alpha}}$ are two sector matrices, then for all $sigmageqsharp$ we have begin{equation*} mathcal{R}(Phi^{1}left( A sigma B)right)leq sec^2alpha~mathcal{R} (Phi(A^{1})sharp Phi(B^{1})).
Keywords: Callebaut inequality, Positive linear map, Sector matrices, Semiselfadjoint mean 
A new modified line search algorithm to solve largescale nonsmooth nonconvex optimization problemPages 6976
In this paper, a new modified line search Armijo is used in the diagonal discrete gradient bundle method to solve largescale nonsmooth optimization problems. The new principle causes the step in each iteration to be longer, which reduces the number of iterations, evaluations, and the computational time. In other words, the efficiency and performance of the method are improved. We prove that the diagonal discrete gradient bundle method converges with the proposed monotone line search principle for semismooth functions, which are not necessarily differentiable or convex. In addition, the numerical results confirm the efficiency of the proposed correction.
Keywords: Nonsmooth optimization, Derivativefree optimization, Diagonal discrete gradient bundle method, line search 
Pages 7782
The Householder iterative scheme (HIS) for determining solution of equations that are nonlinear have existed for over fifty decades and have enjoyed several modifications in literature. However, in most HIS modifications, they usually require function derivative evaluation in their implementation. Obtaining derivative of some functions is difficult and in some cases, it is not achievable.To circumvent this setback, the divided difference operator was utilised to approximate function derivatives that appear in the scheme. This resulted to the development of a new variant of the HIS with high precision and require no function derivative. The theoretical convergence of the new scheme was established using Taylor’s expansion approach. From the computational results obtained when the new scheme was tested on some nonlinear problems in literature, it performed better than the Householder scheme.
Keywords: Nonlinear equation, Iterative scheme, Householder iterative scheme, Derivative free 
Pages 83103
In this paper, we study the existence of at least three distinct solutions for a class of impulsive fractional boundary value problems with $p$Laplacian with Dirichlet boundary conditions. Our approach is based on recent variational methods for smooth functionals defined on reflexive Banach spaces. One example is presented to demonstrate the application of our main results.
Keywords: Fractional $p$Laplacian, Impulsive effects, Three solutions, Variational methods 
Pages 105118
In this paper, we use the spectral element method for solving the stochastic partial differential equation. For spatial discretization, we use the Legendre spectral element method, and we obtain the semidiscrete form. To solve the problem, we need to obtain the complete discrete form and we use the backward Euler method to this aim. The Weiner process is approximated by Fourier series and we obtain the fully discrete scheme of the problem. Error and convergence analysis are presented and, with a numerical example, we demonstrate the efficiency of the proposed method.
Keywords: Stochastic partial differential equation, spectral element method, Legendre polynomials 
Pages 119127
A kind of approximation, called best coapproximation was introduced and discussed in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by several researchers in different abstract spaces. In this paper, we define relations on best coapproximation and worst coapproximation. We show that these relations are equivalence relation. We obtain cosets sets of best coapproximation and worst approximation. We obtain some results on these sets, compactness and weakly compactness and define coqproximinal and coqremotal.
Keywords: Cochebyshev sets, Cosets best coaprrpximation sets, Cosets worst coapproximation, Coqproximinal, Coqremotal, Equivalence relations 
Pages 129142
In this paper, we investigate the COVID19 pandemic in Iran from a mathematical modeling perspective. By improving the wellknown susceptible infected recovered (SIR) family of compartmental models and adding unreported cases obtain a local model for Iran. Since we only want infected cases, we have refused to add other classes which there are can be. we estimate the infected case by using the reported data of the first period of the outbreak and will apply the results to data of the provinces of Ardabil and Guilan which were available to us as well as published data from Iran. We show that, if some of the indexes are constant, the future infectious reported cases are predictable. Also, we show a good agreement between the reported data and the estimations given by the proposed model. We further demonstrate the importance of choosing this proposed model used to by finding the basic reproductive number. Also, we will estimate the probability distribution for the death rate. Our study can help the decisionmaking of public health.
Keywords: Coronavirus pandemic globally, Mathematical modeling, SIRUmodel, Parameter identification, Statistical methods, Akaike information criterion