Some new paranormed sequence spaces and core theorems

Let mu is an element of{l(infinity), c, c(0)}. In this study, by using lambda matrix. and difference matrix B, we introduce the new nonabsolute type paranormed sequence space mu(lambda, B; p) and prove that mu(lambda, B; p) and mu(p) linearly isomorphic. Further, we give some inclusion relations concerning the space mu(lambda, B; p). Afterwards, we determine the alpha-, beta- and gamma-duals of the space mu(lambda, p; B). We also give the characterization of the classes (mu(lambda, B; p) : nu) and (nu : mu(lambda, B; p)), where. is any given sequence space. Moreover, we introduce the Lambda-core of a complex valued sequence and determine the necessary and sufficient conditions on a matrix Lambda for which Lambda- core(Lambda x) subset of K core(x) and Lambda core(Ax) subset of st core(x) for all x subset of l(infinity).