JournalISSN: 0008-4395

Cambridge University Press
About: Canadian Mathematical Bulletin is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Mathematics & Ring (mathematics). It has an ISSN identifier of 0008-4395. Over the lifetime, 4651 publications have been published receiving 43605 citations. The journal is also known as: CMB & Bulletin canadien de mathématiques.

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TL;DR: In this paper, the authors define the spaces l ∞(Δ), c( Δ), and c0(δ) for mapping a matrix A to a matrix C ∞ (Δ) and determine necessary and sufficient conditions for a matrix c ∞ or c( Δ) to map A to map l∞ or C into l ∆ or c, and investigate related questions.
Abstract: In this paper define the spaces l ∞(Δ), c(Δ), and c0(Δ), where for instance l∞(Δ) = {x=(xk):supk |xk -xk + l|< ∞}, and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l ∞(Δ) or c(Δ) into l∞ or c, and investigate related questions.

718 citations

Journal ArticleDOI
TL;DR: The following theorem is the principal result of as discussed by the authors : if (M, d) be a metric space and T a self-mapping of M satisfying the condition for x,y ∊ M 1 where a, b, c, e, f are nonnegative, then α = a+b+c+e+f.
Abstract: The following theorem is the principal result of this paper. Let (M, d) be a metric space and T a self-mapping of M satisfying the condition for x,y ∊ M 1 where a, b, c, e,f are nonnegative and we set α=a+b+c+e+f.

436 citations

Journal ArticleDOI
TL;DR: In this paper, the following result was proved: the Lipschitz constant k < 1 for a complete metric space with fixed points u and un respectively is a contraction mappings of X into itself.
Abstract: The following result is proved in [1, p. 6]. Theorem 1. Let X be a complete metric space, and let T and Tn(n = 1, 2,…)be contraction mappings of X into itself with the same Lipschitz constant k<1, and with fixed points u and un respectively. Suppose that limn → ∞ Tn(x) = T(x) for every x ∊ X. Then limn → ∞ un = u.

400 citations

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TL;DR: In this paper, the authors considered undirected Thomsen graphs, having neither loops nor multiple edges, and considered the problem of gas, water, and electricity in these graphs.
Abstract: A Thomsen graph [2, p. 22] consists of six vertices partitioned into two classes of three each, with every vertex in one class connected to every vertex in the other; it is the graph of the “gas, water, and electricity” problem [1, p. 206]. (All graphs considered in this paper will be undirected, having neither loops nor multiple edges.)

400 citations

Journal ArticleDOI
TL;DR: In this article, the existence of magic valuations for complete graphs was investigated for graphs, which are related to cyclic decompositions of complete graphs into isomorphic subgraphs.
Abstract: The purpose of this paper is to investigate for graphs the existence of certain valuations which have some "magic" property. The question about the existence of such valuations arises from the investigation of another kind of valuations which are introduced in [1] and are related to cyclic decompositions of complete graphs into isomorphic subgraphs. Throughout this paper the word graph will mean a finite undirected graph without loops or multiple edges having at least one edge. By G(m, n) we denote a graph having m vertices and n edges, by V(G) and E(G) the vertex-set and the edge-set of G, respectively. Both vertices and edges are called the elements of the graph.

369 citations

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No. of papers from the Journal in previous years
YearPapers
202334
2022100
202196
202096
201964
201828