On the solvability of the sequence spaces equations of the form (l_a^p)delta+Fx=Fb where F=c_0, c, or l_{infinite}

Abstract

Given a sequence z=(zn) of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y=(yn) such that y/z belongs to E. By delta we denote the operator of the first difference defined by deltan(y)=yn-y(n-1) for all sequences y and all n. In this paper we state some results on the (SSE) of the form l(ap)delta+Fx=Fb p>1, where F=c0, c, or linfinite. We apply these results to the solvability of the (SSE) l(ap)delta+sx=su for u>0, l(rp)delta+s0x=s0b and l(rp)delta+Fx=Fu for r, u>0 and F=c0, c, or linfinite.