On Lacunary Strong (A, u, Delta) - Convergent Sequences with Respect to a Sequence of Modulus Functions

The purpose of this paper is to define and study the spaces N-theta ( A,F,u ,Delta) and N-theta(0) (Lambda,F,u,Delta) of lacunary strong (Lambda,u,Delta)- convergent sequences with respect to a sequence of modulus functions, where A = (a(ik)) is an infinite matrix of complex numbers, u- (u(i)) is an arbitrary sequence such that u(i) (sic) 0,i - 1,2,3,..., and for any sequence x = (x(i)); the difference sequence Delta x is given by Delta x = (Delta(xi))(i=1)(infinity) = (x(i) - x(i-1))(i= 1)(infinity). We also study some inclusioin relations between lacunary strong (A,u,Delta)- convergence and lacunary (A,u,Delta) - statistical convergence. These new spaces will give as aspecial case those spaces defined and studied by T. Bilgin in 2004.