Approximation of periodic functions by Zygmund means in Orlicz spaces

On difference sequence spaces defined by Orlicz functions without convexity

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.  

double sequence spaces defined by orlicz functions

in this paper we introduce some new double sequence spaces using the orlicz function andexamine some properties of the resulting sequence spaces.

Best Simultaneous Approximation in Orlicz Spaces

Some generalized difference sequence spaces of invariant means defined by Orlicz functions

Let l∞ and c denote the Banach spaces of bounded and convergent sequences x = (xk), with xk ∈R or C, normed by ‖x‖ = supk |xk|, respectively. A paranorm on a linear topological space X is a function g : X →R which satisfies the following axioms for any x, y,x0 ∈ X and λ,λ0 ∈ C: (i) g(θ) = 0, where θ = (0,0,0, . . .), the zero sequence, (ii) g(x) = g(−x), (iii) g(x+ y) ≤ g(x) + g(y) (subadditivi...

Sharp estimates of approximation of periodic functions in Hölder spaces

The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the Hölder spaces H p for all 0 < p ≤ ∞ and 0 < α ≤ r. By using modifications of the classical moduli of smoothness, we give improvements of the direct and inverse theorems of approximation and prove the criteria for the precise order of decrease of the best approximation in these spaces. Moreove...