In this paper, we define the space Sαθ (∆mv, f) of all f)-lacunary statistical convergent sequences order α with help unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number ∈ (0, 1]. We also introduce ωαθ strong summable α. Properties related to these spaces are studied. Inclusion relations between ωα θ established under certain conditions.

We prove L(w) bounds for the Carleson operator C, its lacunary version Clac, and its analogue for the Walsh series W in terms of the Aq constants [w]Aq for 1 q p. In particular, we show that, exactly as for the Hilbert transform, ‖C‖Lp(w) is bounded linearly by [w]Aq for 1 q < p. We also obtain L(w) bounds in terms of [w]Ap , whose sharpness is related to certain conjectures (for instance, of K...

Organothiophosphoryl polyoxotungstates R(contains)XW(infinityinfinity)O(contains exists) (/-) , R(contains) P(contains)W(infinity),O(infinity) (/-), R(contains)PW( exists)O(contains) (Delta) (-)(X = P, Si, Ge, B or Ga; R = PhP(S), C(6)H(11)P(S)) have been prepared from lacunary polyoxoanions and PhP(S). The products were characterized by elemental analysis, IR, and NMR spectroscopy. According t...

A well known theorem states as follows :' Let ni < n2 <. . ., nk+1 / nk > A > 1 be an infinite sequence of real numbers and S (ak + bk) a divergent series satisfying k=1 Then denotes the Lebesgue measure of the set in question. It seems likely that the Theorem remains true if it is not assumed that the n k are integers. On the other hand if nk ,f-n,.-1 is an arbitrary sequence of integers it is...

In this article, we introduce the lacunary difference sequence spaces w0(M , θ,∆ n m, p, q), w1(M , θ,∆ n m, p, q) and w∞(M , θ,∆ n m, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of qlacunary ∆nm-statistical convergent sequences. Further, we study the relationship between q-lacunary ∆nm-statis...

In this article we introduce and study the notions of ( , ) s v r  -lacunary strongly summable, ( , ) s v r  Cesàro strongly summable, ( , ) s v r  statistically convergent and ( , ) s v r  -lacunary statistically convergent sequence of fuzzy numbers. Consequently we construct the spaces   ( , ) F sv r L  ,   1 ( , ) F sv r   ,   ( , ) F sv r S  and   ( , ) F sv r S  respecti...

In this article we introduce the concepts of lacunary Iconvergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.

We describe some combinatorial problems in finite projective planes and indicate how Rédei’s theory of lacunary polynomials can be applied to them. 2000 Mathematics Subject Classification: 05.