Lacunary statistical convergence of order α,β for generalized vector-valued difference sequence spaces

In this paper, we defined space S theta alpha,beta</mml:msubsup>(Delta vm</mml:msubsup>,E,q) of all vector-valued lacunary Delta vm</mml:msubsup>-statistical convergent sequences of order (alpha,beta) and space N theta alpha,beta</mml:msubsup>(Delta vm,E,q,p) of all vector-valued strongly Delta vm-lacunary summable sequences of order (alpha,beta) by taking sequence (<mml:msub>Ek,<mml:msub>qk) of normed spaces, where p is a positive real number and alpha,beta are real numbers with 0<<alpha>beta 1. Some inclusion relations between these spaces are obtained. We also studied space omega theta alpha,beta(Delta vm,f,E,q,p) of all vector-valued strongly Delta vm-lacunary summable sequences of order (alpha,beta) with respect to modulus function f by taking a bounded sequence (<mml:msub>pk) of strictly positive real numbers with <mml:mstyle displaystyle="true" scriptlevel="0"><mml:munder>infk</mml:munder><mml:msub>pk>0</mml:mstyle>. The inclusion relations between spaces omega theta alpha,beta(Delta vm,f,E,q,p) and S theta alpha,beta(Delta vm,E,q) are determined.