Displaying similar documents to “A convergent nonlinear splitting via orthogonal projection”

On the convergence theory of double K -weak splittings of type II

Vaibhav Shekhar, Nachiketa Mishra, Debasisha Mishra (2022)

Applications of Mathematics

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Recently, Wang (2017) has introduced the K -nonnegative double splitting using the notion of matrices that leave a cone K ⊆ ℝ n invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for K -weak regular and K -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory...

Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations

Monnanda Erappa Shobha, Ioannis K. Argyros, Santhosh George (2014)

Applicationes Mathematicae

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We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is y δ with | | y - y δ | | ≤ δ , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where F ' ( x ₀ ) - 1 exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator....

Existence results and iterative method for fully third order nonlinear integral boundary value problems

Quang A Dang, Quang Long Dang (2021)

Applications of Mathematics

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We consider the boundary value problem u ' ' ' ( t ) = f ( t , u ( t ) , u ' ( t ) , u ' ' ( t ) ) , 0 < t < 1 , u ( 0 ) = u ' ( 0 ) = 0 , u ( 1 ) = ∫ 0 1 g ( s ) u ( s ) d s , where f : [ 0 , 1 ] × ℝ 3 → ℝ + , g : [ 0 , 1 ] → ℝ + are continuous functions. The case when f = f ( u ( t ) ) was studied in 2018 by Guendouz et al. Using the fixed-point theory on cones they established the existence of positive solutions. Here, by the method developed by ourselves very recently, we establish the existence, uniqueness and positivity of the solution under easily verified conditions and propose an iterative method for finding the solution. Some examples demonstrate the validity of the...

Some cohomological aspects of the Banach fixed point principle

Ludvík Janoš (2011)

Mathematica Bohemica

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Let T : X → X be a continuous selfmap of a compact metrizable space X . We prove the equivalence of the following two statements: (1) The mapping T is a Banach contraction relative to some compatible metric on X . (2) There is a countable point separating family ℱ ⊂ 𝒞 ( X ) of non-negative functions f ∈ 𝒞 ( X ) such that for every f ∈ ℱ there is g ∈ 𝒞 ( X ) with f = g - g ∘ T .

Positive solution for a quasilinear equation with critical growth in ℝ N

Lin Chen, Caisheng Chen, Zonghu Xiu (2016)

Annales Polonici Mathematici

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We study the existence of positive solutions of the quasilinear problem ⎧ - Δ N u + V ( x ) | u | N - 2 u = f ( u , | ∇ u | N - 2 ∇ u ) , x ∈ ℝ N , ⎨ ⎩ u(x) > 0, x ∈ ℝ N , where Δ N u = d i v ( | ∇ u | N - 2 ∇ u ) is the N-Laplacian operator, V : ℝ N → ℝ is a continuous potential, f : ℝ × ℝ N → ℝ is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.

An iterative construction for ordinary and very special hyperelliptic curves

Francis J. Sullivan (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si costruiscono famiglie di curve iperellittiche col p —rango della varietà jacobiana uguale a zero. La costruzione sfrutta le proprietà elementari dell’operatore di Cartier e delle estensioni p -cicliche dei corpi con la caratteristica p maggiore di zero.