Abstract:In the present work the generalized weighted mean difference operator Gu,v;Δ has been introduced by combining the generalized weighted mean and difference operator under certain special cases of sequences u=(uk) and v=(vk). For any two sequences u and v of either constant or strictly decreasing real numbers satisfying certain conditions the difference operator Gu,v;Δ is defined by (G(u,v;Δ)x)k=∑i=0kukvi(xi-xi-1) with xk=0 for all k<0. Furthermore, we compute the spectrum and the fine spectrum of the opera… Show more
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