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Nonlinear contractions in metrically convex space
Publicationes Mathematicae Debrecen, 1994Summary: We prove among other things the following fixed point theorem. Let \(T\) be a selfmapping of a complete Menger convex metric space \((X, d)\) and \(\psi: [0, \infty)\to [0, \infty)\) a function such that \[ d(T(x), T(y))\leq \psi(d(x, y)),\qquad (x, y\in X). \] Suppose that \(\psi\) is continuous at 0 and that there exists a positive sequence \
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Pseudo strict convexity and metric convexity in metric linear spaces
Let (X,d) be a real metric linear space. Then d defines a strictly convex norm on X if and only if the following two conditions are satisfied: (i) for distinct x,y in X there exists z (different from x,y) such that \(d(x,z)+d(z,y)=d(x,y)\); and (ii) if x,y are non-zero such that \(d(x+y,0)=d(x,0)+d(y,0)\) then \(y=tx\) for some \(t>0.\) The case of ...Sastry, K. P. R. +2 more
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Metric Entropy of Convex Hulls in Hilbert Spaces
Bulletin of the London Mathematical Society, 1997Summary: Let \(X\subset H\) be a precompact subset of a Hilbert space and let \(N (\varepsilon,X)\), \(\varepsilon>0\), denote the minimal number of balls of radius \(\varepsilon\) covering the set \(X\). In the paper, the following asymptotically optimal result is shown: If \(N (\varepsilon,X)= O(\varepsilon^{-\alpha})\) as \(\varepsilon \uparrow 0\),
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One step iterative scheme for a pair of nonexpansive mappings in a convex metric space
, 2015Hafiz Salah ud Din
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Common Fixed Point Iterations of Non-Lipschitzian Mappings in a Convex Metric Space
, 2016H. Fukhar-ud-din, J. Nieto, A. Khan
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Multifunctional biomolecule nanostructures for cancer therapy
Nature Reviews Materials, 2021Jing Wang, Yiye Li, Guangjun Nie
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Cosmology with the Laser Interferometer Space Antenna
Living Reviews in Relativity, 2023Germano Nardini
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Fixed point results in convex metric spaces
Journal of Fixed Point Theory and Applications, 2019Keerati Siriyan, A. Kangtunyakarn
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