Keywords: Bernstein operators Pointwise approximation Rate of convergence a b s t r a c t In the present paper, we study pointwise approximation by Bernstein–Durrmeyer type operators in the mobile interval x 2 0; 1 À 1 nþ1 h i , with use of Peetre's K-functional and x 2 u k ðf ; tÞ ð0 6 k 6 1Þ, we give its properties and obtain the direct and inverse theorems for these operators.

in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1

In the present article, we extend our study of Kantorovich type exponential sampling operators introduced in [4]. We derive Voronovskaya theorem and its quantitative estimates for these terms an appropriate K-functional. Further, improve order approximation by using convex linear combinations operators. Finally, provide few examples kernels along with graphical representations.

We introduce a genuine summation-integral type operators based on Lupaş-Jain base functions related to the unbounded sequences. investigated their degree of approximation in terms modulus continuity and ????-functional for from bounded continuous space. Furthermore, we give some theorems local properties belonging Lipschitz class. Also, Voronovskaja theorem these operators.

1. Topological Vector Spaces 1 2. Banach Algebras 10 2.1. ∗–Algebras (over complexes) 15 2.2. Exercises 18 3. The Spectral Theorem 19 3.1. Problems on the Spectral Theorem (Multiplication Operator Form) 24 3.2. Integration with respect to a Projection Valued Measure 25 3.3. The Functional Calculus 32 4. Unbounded Operators 35 4.1. Closed, symmetric and self-adjoint operators 35 4.2. Differentia...

The logic programming community has a love{hate relationship with operators for pruning the search space of logic programs such as cut, commit, once, conditionals and variations on these. Pruning operators typically are not declarative, result in incom-pleteness and/or unsoundness, decrease readability and exibility of code and make program analysis and transformation more diicult. Despite this...

This paper briefly describes process functional language compiler architecture. Process functional language is an experimental functional language with imperative features like memory cell variables. The main parts of the process functional language compiler are presented with short description and examples. Current implementation of PFL compiler comprises a algebraic types, primitive functions...

For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation leading the LPDE to the separation of variables (SoV). The auxiliary operators are found for various types of the SoV including conventional SoV in the scalar second order LPDE and the SoV by the fun...

Discrete versions of basic inequalities in functional analysis such as the Sobolev inequality play key role in theoretical analysis of finite difference schemes. They have been shown for some simple difference operators, but are still left open for general operators, even including the standard central difference operators. In this paper, we propose a systematic approach for deriving such inequ...