A note about the relation between fixed point theory on cone metric\n spaces and fixed point theory on metric spaces

2011/11/14 by Ion Marian Olaru, Olaru, Ion
Mathematics · Medicine · Physics and Astronomy · #47H10 #Advanced Differential Geometry Research #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Lipid metabolism and disorders

paper · pdf · doi:10.48550/arxiv.1111.3356

openalex publication_date 2011/11/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let Y be a locally convex Hausdorff space, K \⊂ E a cone and \≤_K the\npartial order defined by K. Let (X, p) be a TV S- cone metric space, \φ : K\n\→ K a vectorial comparison function and f : X \→ X such that\np(f(x), f(y)) \≤_K \φ(p(x, y)), for all x, y \∈ X. We shall show that\nthere exists a scalar comparison function \ψ : R+ \→ R+ and a\nmetric d_p(in usual sense) on X such that d_p(f(x), f(y)) \≤ \ψ(d_p(x,\ny)), for all x, y \∈ X. Our results extend the results of Du (2010) [Wei-Shih\nDu, A note on cone metric fixed point theory and its equivalence, Nonlinear\nAnal. 72 (2010), 2259-2261].\n

Citations

• On nonlinear contractions

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