1 Fourier Transform 1 1.1 Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schwartz space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Convergence in S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourier Transform in L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Fouri...

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

In this paper, first we use an example to show the efficiency of $M$ iteration process introduced by Ullah and Arshad [4] for approximating fixed points of Suzuki generalized nonexpansive mappings. Then by using $M$ iteration process, we prove some strong and $Delta -$convergence theorems for Suzuki generalized nonexpansive mappings in the setting of $CAT(0)$ Spaces. Our results are the extensi...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency Ω is chosen to scale with the order as Ω = CN ; 1/3 < γ < 1/2, C > 0 as N → ∞. It converges also for γ = 1/3, if C ≥ αcg, αc ≃ 0.570875, where g is the coupling constant in front of the operator q/4. The extreme case...

Numerical theory provides the basis for quantification on the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in COMSOL 5.1 to perform computational studies for an elliptic test problem in two and three space dimensions that demonstrate this theory by computing the convergence order of the...

We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the single-well anharmonic oscillator the uniformity of convergence in g ∈ [0,∞] is proven. The convergence proof is extended also to complex values of g lying on a wide do...