Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces

In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M}}}_{p(\cdot),\lambda(\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$.

Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces

Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.

Weighted Simultaneous Approximation of the Linear Combinations of Baskakov Operators

In this paper, the approximation property of the linear combinations of Baskakov operators is investigated by using a Jacobi weight function. Moreover, both the positive and inverse theorems for the weighted simultaneous approximation of the linear combinations of Baskakov operators are proved.

Social semiotics analysis of Palestinian mathematics textbooks for eighth grade

Mathematics textbook analysis can serve to understand the teaching and learning processes in the mathematics classroom. The present study utilizes a social semiotics framework to analyze the triangle unit of the Palestinian mathematics book for grade 8. The results of the study indicate that the authors utilized the representational aspect of the mathematical object to introduce those objects to the reader. Moreover, the nature of mathematics resulting from this unit is that of a subject that learners do not need material processes to discover, so it is enough to reason about it mentally to arrive at the mathematical objects and relations. The authors used a plural first-person pronoun to describe the need to engage with theorems and inverse theorems. They used the singular second-person pronoun to attract the attention of the reader to specific features of the mathematical objects. The authors did not use any pronoun when stating the theorem. Some of the connectors were verbs, nouns, and sentences, where the most used connector was the sentence, especially in reasoning. This use of the sentence in mathematical reasoning indicates that the authors wanted to advance the mathematical reasoning as a narrative to facilitate it for the reader.

Direct and inverse theorems of approximation theory

In this paper, we prove analogues of direct and some inverse theorems, for the Dunkl harmonic analysis, using the function with bounded spectrum and generalized spherical mean operator.