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- W1887896316 abstract "Given a Vilenkin group G, a scalar matrix $Lambda = [lambda_{ij}]_{i in mathbb {N} , j in mathbb{N}_0}$ ,a function $f in L^1(G)$, and a point $x in G$ we introduce, for each $alpha in mathbb{R}$, the $(Lambda,alpha)$ − derivative $f$ at $x$ denoted by $f^{(Lambda,alpha)}(x)$. We also introduce the sets: $$M_alpha = M(G,Lambda,alpha,x) :={ f in L^1(G)：exists f^{(Lambda,alpha)}(x)},$$ $$M=M(G,Lambda,x) := {f in L^1(G)：exists f^Lambda(x)};$$ where $f^Lambda(x)$ derivative in [8], which is a generalization of Onneweer’s derivative $f^{[1]}(x)$ in [6]. We proved: (a) Five theorems which express essential characteristics of $(Lambda,alpha)$− derivative, (b) $M = M_0$, (c) $(forall alpha,beta in mathbb{R}) wedge (alpha < beta)Rightarrow (M_alpha subseteq M_beta) wedge (M_beta setminus M_alpha not= theta)$. Statement b) states that the method $(Lambda,alpha)$ − differentiation, for $alpha=0$, is equal to $Lambda$ − differentiation and statement c) says that $(Lambda,alpha)$− differentiation increases with increasing $alpha in mathbb{R}$." @default.
- W1887896316 created "2016-06-24" @default.
- W1887896316 creator A5049480030 @default.
- W1887896316 date "2011-01-12" @default.
- W1887896316 modified "2023-09-28" @default.
- W1887896316 title "DIFFERENTIATION ON VILENKIN GROUPS USING A MATRIX" @default.
- W1887896316 cites W1995968002 @default.
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- W1887896316 doi "https://doi.org/10.11650/tjm.15.2011.1441" @default.
- W1887896316 hasPublicationYear "2011" @default.
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