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AbstractIn this paper, we generalize the concepts of convexity, strict convexity and uniform convexity in the sense of non-Newtonian calculus. The main aim of this study is to obtain the non-Newtonian convexity, non-Newtonian strict convexity and non-Newtonian uniform convexity properties of the non-Newtonian sequence spaces lp(N).

In this paper, we define the superposition operator Pg where g : N2 x R ? R by Pg((xks))=g(k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized Pg : lp ? l1 and Pg : lp ? lq where 1 ? p,q < ?, respectively. The main goal of this paper is to construct the necessary and sufficient conditions for the continuity of Pg: Lp ? L1 and Pg : Lp ? Lq where 1 ? p,q < ?.

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Let 1 Ä q; p < 1 and v; w be Beurling's weight functions on R d. In this article we deal with harmonic properties of intersection space A