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Let X be a Banach space and let Y be a separable Lindenstrauss space. We describe the Banach space P (Y, X) of absolutely summing operators as a general L1-tree space. We also characterize the BOUNDED APPROXIMATION PROPERTY and its weak version for X in terms of the space of integral operators I (X, Z*) and the space of nuclear operators N (X, Z*), respectively, where Z is a Lindenstrauss space, whose dual Z* fails to have the Radon-Nikod´ym PROPERTY.

Please click on PDF file in Persian to view the abstract.

In this paper, we propose a new method for solving the stochastic advection-diffusion equation of Ito type. In this work, we use a COMPACT finite difference APPROXIMATION for discretizing spatial derivatives of the mentioned equation and semi-implicit Milstein scheme for the resulting linear stochastic system of differential equation. The main purpose of this paper is the stability investigation of the applied method. Finally, some numerical examples are provided to show the accuracy and efficiency of the proposed technique.

Purpose: The purpose of the present paper is to study the Stancu-type generalization of complex Favard-Szasz-Mirakjan operators and establish some APPROXIMATION results in complex domain.Methods: It is observed that the complex Favard-Szasz-Mirakjan-Stancu operators can be written in the form of divided differences. Thus, it is possible to study such operators in complex domain. We use analytical method to obtain our results.Results: We have estimated the order of simultaneous APPROXIMATION, Voronovskaja-type results with quantitative estimates for the complex Favard-Szasz-Mirakjan-Stancu operators attached to analytic functions on COMPACT disks. Also, some estimates on the rate of convergence are given.Conclusions: The results proposed here are new and have better rate of convergence.