On the OrliczCesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.

Several inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. For this the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, see [9], the third one is a consequence of a certain Gaussian-Jensen’s majorization technique, see [6], and the f...

In this paper, following the methods of Connor, we introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure, double infinite matrix and an Orlicz function in 2normed spaces which have unique non-linear structure and examine some of their properties.

In this article, we introduce the notion of statistically pre-Cauchy double sequence of fuzzy numbers. Then we present a characterization of the class of bounded statistically pre-Cauchy double sequences of fuzzy numbers with the help of Orlicz function. Further, we present a characterization of the class of bounded statistically convergent double sequences of fuzzy numbers and linked with Cesà...

and Applied Analysis 3 Put LM X { u ∈ XT : ρM λu < ∞ for some λ > 0 } . 1.5 Then the Musielak-Orlicz-Bochner function space ‖u‖ inf k>0 1 k [ 1 ρM ku ] 1.6 is Banach space. If X R, LM R is said to be Musielak-Orlicz function space. Set K u { k > 0 : 1 k ( 1 ρM ku ) ‖u‖ } . 1.7 In particular, the set K u can be nonempty. To show that, we give a proposition. Proposition 1.1. If limu→∞ M t, u /u ∞...

It is shown that if the Boyd indices of the rearrangement invariant Banach function space Lρ(R) are strictly between 0 and 1, ρ is an absolutely continuous function norm, Ω is a domain from R satisfying the restricted cone condition, denoting by ω the restriction of ρ to Ω, there exists an extension operator for the abstract Sobolev space W Lω(Ω). This is a generalization to abstract Sobolev sp...

In this work we investigate the approximation problems in the Smirnov-Orlicz spaces in terms of the fractional modulus of smoothness. We prove the direct and inverse theorems in these spaces and obtain a constructive descriptions of the Lipschitz classes of functions defined by the fractional order modulus of smoothness, in particular. 1. Preliminaries and introduction A function M (u) : R → R ...

We show that a general Walsh series is the Walsh-Fourier series of a function f ∈ Lp[0, 1] for 1 ≤ p <∞ if and only if its sequence of partial sums contains a relatively weakly compact subsequence. Several other criteria are established for the case where f ∈ LΦ[0, 1], the Orlicz space generated by an N -function Φ. Mathematics subject classification (2000): 42C10, 46E30

Let χ denotes the space of all double gai sequences. Let Λ denotes the space of all double analytic sequences. This paper is devoted to a study of the general properties of Nörlund double Orlicz space of gai sequence space η ( χM ) and χM . and Nörlund double Orlicz space of analytic sequence space η ( ΛM ) and ΛM .

In the present paper we provide the decomposition and local estimates for the pressure function for the non-stationary flow of incompressible non-Newtonian fluids in Orlicz spaces. We show that this method can be applied to prove the existence of weak solutions to the problem of motion of one or several rigid bodies in a non-Newtonian incompressible fluid with growth conditions given by an N -f...