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In this paper, we deal with the existence and multiplicity
solutions, for the following fractional  discrete boundary-value problem
begin{equation*}
begin{cases}
_{T+1}nabla_k^{alpha}left( ^{}_knabla_{0}^{alpha}(u(k))right)+{^{}_knabla}_{0}^{alpha}left( ^{}_{T+1}nabla_k^{alpha}(u(k))right)=lambda f(k,u(k)), quad k in [1,T]_{mathbb{N}_{0}},
u(0)= u(T+1)=0,
end{cases}
end{equation*}
where $0leq alphaleq1$ and $^{}_{0}nabla_k^{alpha}$ is  the left nabla discrete fractional difference  and $^{}_knabla_{T+1}^{alpha}$ is the right nabla discrete fractional difference  and   $f: [1,T]_{mathbb{N}_{0}}timesmathbb{R}tomathbb{R}$ is
a continuous function and $lambda>0$ 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.
textbf{MSC(2010):} 26A33; 39A10; 39A27.
textbf{Keywords:}  Discrete fractional calculus, Discrete nonlinear boundary
value problem, Non trivial solution, Variational methods, Critical
point theory. 

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Abstract. Let X be a separable Banach space and M be a subspace of X. A bounded Linear operator T on X is subspace balanced convex-cyclic 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 convex-cyclic operator that is not balanced convex-cyclic. Also we give an improvement of the Kitailike criterion for subspace balanced convex-cyclicity and bring on with the Hahn-Banach characterization for subspace balanced convex-cyclicity.

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 In this paper we give a topology-dynamical 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.

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In the current paper, we study an inverse problem of identifying a time-dependent forcing term in the one-dimensional 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 well-conditioned 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.
 

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In this paper, we study the conformal transformation of some important and effective non-Riemannian 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 non-Riemannian curvature  H.

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The main goal of this paper is to discuss the Callebaut inequality and mean-convex 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})).

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‎In this paper‎, ‎a new modified line search Armijo is used in the diagonal discrete gradient bundle method to solve large-scale non-smooth 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 semi-smooth functions‎, ‎which are not necessarily differentiable or convex‎. ‎In addition‎, ‎the numerical results confirm the efficiency of the proposed correction‎.

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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 semi-discrete 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.

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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 non-linear problems in literature, it performed better than the Householder
scheme.
 

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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.

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In this paper, we investigate the COVID-19 pandemic in Iran from a mathematical modeling perspective. By improving the well-known 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 decision-making of public health.

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ln this paper, we introduce an iterative scheme for approximating a common element of the fixed point sets of a finite family of a multivalued -hemicontractive mappings, the set of solutions of a finite family of variational inequality problems and the set of solutions of a finite family of equilibrium problems. Using our scheme, we establish strong convergence theorems of the aforementioned problems in the framework of real Hilbert spaces. Our results improve, extend, generalise and unify many recent results in this direction.

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We introduce an iterative algorithm for split equality fixed point and null point problem for Lipschitzian quasi-pseudocontractive
mappings and maximal monotone operators which includes split equality feasibility problem, split equality fixed problem, split equality null point
problem and other problem related to fixed point problems. Moreover, we establish a strong convergence results in real Hilbert spaces under
some suitable conditions and reduce our main result to above-mentioned problems. Finally, we apply the study to split equality feasibility problem (SEFP), split equality equilibrium problem (SEEP), split equality variational inequality problem (SEVIP) and split equality optimization problem (SEOP). The results presented in the paper extend and improve many recent results.

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In this paper, we use some bi-sequences of positive numbers to define weighted dynamical metrics. Then we show that, replacing the Bowen dynamical metric by the weighted metric, the definition of pressure for asymptotically sub-additive potentials, including measure-theoretic and topological, is not affected. This generalizes some known results for pressure, defined using mean metrics and continuous potentials.

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In this paper, we deal with the existence of a non-trivial
solution for the following fractional  discrete boundary-value problem for any $k in [1,T]_{mathbb{N}_{0}}$
begin{equation*}
begin{cases}
_{T+1}nabla_k^{alpha}left( ^{}_knabla_{0}^{alpha}(u(k))right)+{^{}_knabla}_{0}^{alpha}left( ^{}_{T+1}nabla_k^{alpha}(u(k))right)+phi_{p}(u(k))=lambda f(k,u(k)),
 u(0)= u(T+1)=0,
end{cases}
end{equation*}
where $0< alpha<1$ and $^{}_knabla_{0}^{alpha}$ is  the left nabla discrete fractional difference  and $^{}_{T+1}nabla_k^{alpha}$ is the right nabla discrete fractional difference   $f: [1,T]_{mathbb{N}_{0}}timesmathbb{R}tomathbb{R}$ is
a continuous function, $lambda>0$ is a parameter and  $phi _{p}$ is the so called $p$-Laplacian
operator defined as $phi _{p}(s)=|s|^{p-2}s$ and $1

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A bounded linear operator T on a locally convex space X is balanced convex-cyclic if there exists a vector x 2 X such that the balanced convex hull of orb(T; x) is dense in X.A balanced convex-polynomial is a balanced convex combination of monomials f1; z; z²; z³; : : : g.In this paper we prove that the balanced convex-polynomials are dense in Lp() when ([-1; 1]) = 0.Our results are used to characterize which multiplication operators on various real Banach spaces are balanced convex-cyclic.Also,it is shown for certain multiplication
operators that every nonempty closed invariant balanced convex-set is a closed invariant subspace.

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The class of Bryant-type metrics is a  natural extension of the class of 4-th root Finsler metrics which are used in Biology as ecological metrics. In this paper, we  classify  Bryant-type metrics admitting an $(alpha, beta)$-metric on a two-dimensional  manifold and show that it contains two classes of non-Riemannian $(alpha, beta)$-metrics, specially Randers-type metrics. This might provide fine insights into a possible theory of deformations of Finsler norms.

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Data Envelopment Analysis (DEA) is a Nonparametric method for measuring of the performance of decision-making units (DMUs) - which do not need to have or compute a firm's production function, which is often difficult to calculate. In this article, we evaluate the units under review in terms of cost efficiency, and the units in terms of spending and production over several periods, and the rate of improvement or regression of each of these units. Considering the minimal use of resources and consuming less money, the improvement or retreat of the recipient's decision unit in terms of cost was examined by presenting a method based on solving linear programming models using the productivity index is Malmquist Global. Finally, by designing and solving a numerical example, we emphasize and test the applicability of the material presented in this article.

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The paper is devoted to continuous frames and continuous Riesz basis in Hilbert C*-modules. We define a continuous Riesz basis in Hilbert C*-modules and investigate the relationship between a continuous Riesz basis and an L^2-independent Bessel mapping. Also, we show that a continuous frame is a continuous Riesz basis if and only if it is a Riesz-type frame. Finally, we give the relation between two continuous Riesz bases in Hilbert C*-modules.

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This paper tries to show that there is only one solution for problem of fractional $q$-differential equations with  Hilfer type, and it does so by using a particular method known as Schaefer's fixed point theorem  and the Banach contraction principle. After that, we create a integral  type of the  problem for nonlocal condition. Next, we show that Ulam stability is true. The Gr"{o}wnwall rule for singular kernels of the equations helps to show our findings are correct. We confirm our findings by giving a few practical examples.