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

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.

In this paper we are concerned with cuts in models of Samuel Buss’ theories of BOUNDED arithmetic, i.e. theories like Si2 and Ti2. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are BOUNDED above by a small element. We study the basic PROPERTIES of pcuts and small cuts. In particular, we prove some overspill and underspill PROPERTIES for them.

In this paper, we give a generalization of the Baskakov-type operators introduced by Baskakov (Doklady Akademii Nauk SSSR 113:249–251, 1957 (in Russian)) and obtain some direct and inverse results for these new operators.

Algebraic frames are generalizations of Fourier transforms on locally compact abelian groups in the sense that the family of vectors forming the frame are replaced by a family of unBOUNDED linear functionals. The paper studies the indexing measure space of the algebraic frames; as the investigation narrows down to the class of lower semiframes, more relations are revealed between the discreteness and the redundancy of the frame family.

The purpose of this paper is to study the bivariate extension of the generalized Baskakov-Kantorovich operators and obtain results on the degree of APPROXIMATION, Voronovskaja type theorems and their first order derivatives in polynomial weighted spaces. Furthermore, we illustrate the convergence of the bivariate operators to a certain function through graphics using Matlab algorithm. We also discuss the comparison of the convergence of the bivariate generalized Baskakov Kantorovich operators and the bivariate Sz\'{a}sz-Kantorovich operators to the function through illustrations using Matlab.

Purpose: The purpose of this paper is to introduce and study the Baskakov- Durrmeyer- Stancu operators based on q-integers.Methods: First we use property of q-calculus to estimate moments of these operators. Also study some APPROXIMATION PROPERTIES, asymptotic formula including q-derivative and point-wise estimation for the operators L(a,b)n,q .Results: We studied better error estimations for these operators using King type approach.Conclusions: The results proposed here are new and have a better rate of convergence.

Purpose: To study the rate of convergence of q analogue of Durrmeyer operator generalization proposed by N. Deo.Methods: We first estimatemoments of q-Durrmeyer operators. We also study the rate of convergence our operators.Results: We use Maple programming to draw the graphs for the APPROXIMATION process for two operators. In all graphs, we observe that either classical operator has sharp convergence or both operators behave alike after a large number of iterations.Conclusions: We conclude that the modified operator does not improve the APPROXIMATION process.