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On the iterates of positive linear operators
Let \(U\) be a positive linear operator on \(C[0,1]\) that leaves the linear functions, \(P^1\), invariant. The paper presents a simple short proof of the following: Theorem: If there is a continuous function \(f\) such that \(Uf-f\) has no zeros in \((1,0)\) then \(U^k g\) converges to the projection onto \(P^1\) that interpolates to \(g\) at \(0 ...
Dumitru Mircea Ivan, Ioan Gavrea
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Summation process of positive linear operators
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C Orhan
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Eventually positive semigroups of linear operators
We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy problem is positive for large enough time.
James B Kennedy +2 more
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Positive linear operators and exponential functions
Mathematical Foundations of Computing, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ana Maria Acu, Ioan Rasa, Andra Seserman
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On a Class of Positive Linear Operators
Canadian Mathematical Bulletin, 1973In a recent paper [3] Meir and Sharma introduced a generalization of the Sα- method of summability. The elements of their matrix, (ank), are defined by(1)where is a sequence of complex numbers. if 0 < αj < l for each j = 0, 1, 2,… then ank≥0 for each n = 0, 1, 2,… and k = 0,1,2,…
Swetits, J., Wood, B.
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Matrix Summability and Positive Linear Operators
Positivity, 2007The continuous function \(\rho: \mathbb{R}\to\mathbb{R}\) is called weight function if \(\lim_{|x|\to\infty} \rho(x)=+\infty\) and \(\rho(x)\geq 1\) for all \(x\in\mathbb{R}\). The weighted space \(B_\rho\) contains the all real-valued functions \(f\) defined on \(\mathbb{R}\) for which \(|f(x)|\leq M_f\cdot\rho(x)\) for every \(x\in\mathbb{R}\) (\(M_f\
Atlihan, Özlem G., Orhan, Cihan
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