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Relevant bibliographies by topics / Frechet derivative, Banach spaces

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Academic literature on the topic 'Frechet derivative, Banach spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Frechet derivative, Banach spaces"

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Mirotin, A. R. "Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus." Filomat 34, no. 4 (2020): 1105–15. http://dx.doi.org/10.2298/fil2004105m.

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We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove the formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces is investigated. The results may be regarded as a contribution to the Hirsch functional calculus.

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Mirotin, A. R. "Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus." Filomat 34, no. 4 (2020): 1105–15. http://dx.doi.org/10.2298/fil2004105m.

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We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove the formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces is investigated. The results may be regarded as a contribution to the Hirsch functional calculus.

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PRASHANTH, M., and D. K. GUPTA. "A CONTINUATION METHOD AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES." International Journal of Computational Methods 10, no. 04 (April 23, 2013): 1350021. http://dx.doi.org/10.1142/s0219876213500217.

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A continuation method is a parameter based iterative method establishing a continuous connection between two given functions/operators and used for solving nonlinear equations in Banach spaces. The semilocal convergence of a continuation method combining Chebyshev's method and Convex acceleration of Newton's method for solving nonlinear equations in Banach spaces is established in [J. A. Ezquerro, J. M. Gutiérrez and M. A. Hernández [1997] J. Appl. Math. Comput.85: 181–199] using majorizing sequences under the assumption that the second Frechet derivative satisfies the Lipschitz continuity condition. The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the convergence analysis of such a method. This leads to a simpler approach with improved results. An existence–uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α ∈ [0, 1]. Four numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness region and error bounds for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in three examples, whereas in one example it gives the same results. Further, we have observed that for particular values of the α, our analysis reduces to those for Chebyshev's method (α = 0) and Convex acceleration of Newton's method (α = 1) respectively with improved results.

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Talakua, Mozart W., and Stenly J. Nanuru. "TEOREMA REPRESENTASI RIESZ–FRECHET PADA RUANG HILBERT." BAREKENG: Jurnal Ilmu Matematika dan Terapan 5, no. 2 (December 1, 2011): 1–8. http://dx.doi.org/10.30598/barekengvol5iss2pp1-8.

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Hilbert space is a very important idea of the Davids Hilbert invention. In 1907, Riesz and Fréchet developed one of the theorem in Hilbert space called the Riesz-Fréchet representationtheorem. This research contains some supporting definitions Banach space, pre-Hilbert spaces, Hilbert spaces, the duality of Banach and Riesz-Fréchet representation theorem. On Riesz-Fréchet representation theorem will be shown that a continuous linear functional that exist in the Hilbert space is an inner product, in other words, there is no continuous linear functional on a Hilbert space except the inner product.

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Osinuga, I. A., S. A. Ayinde, J. A. Oguntuase, and G. A. Adebayo. "On Fermat-Torricelli Problem in Frechet Spaces." Journal of Nepal Mathematical Society 3, no. 2 (December 30, 2020): 16–26. http://dx.doi.org/10.3126/jnms.v3i2.33956.

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We study the Fermat-Torricelli problem (FTP) for Frechet space X, where X is considered as an inverse limit of projective system of Banach spaces. The FTP is defined by using fixed countable collection of continuous seminorms that defines the topology of X as gauges. For a finite set A in X consisting of n distinct and fixed points, the set of minimizers for the sum of distances from the points in A to a variable point is considered. In particular, for the case of collinear points in X, we prove the existence of the set of minimizers for FTP in X and for the case of non collinear points, existence and uniqueness of the set of minimizers are shown for reflexive space X as a result of strict convexity of the space.

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Zheng, Xi Yin. "Very Differentiable and Generic Frechet Differentiable Convex Functions on Banach Spaces." Journal of Mathematical Analysis and Applications 235, no. 1 (July 1999): 168–79. http://dx.doi.org/10.1006/jmaa.1999.6388.

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Jokhadze, O. "Spatial Problem of Darboux Type for One Model Equation of Third Order." gmj 3, no. 6 (December 1996): 547–64. http://dx.doi.org/10.1515/gmj.1996.547.

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Abstract For a hyperbolic type model equation of third order a Darboux type problem is investigated in a dihedral angle. It is shown that there exists a real number ρ0 such that for α > ρ0 the problem under consideration is uniquely solvable in the Frechet space. In the case where the coefficients are constants, Bochner's method is developed in multidimensional domains, and used to prove the uniquely solvability of the problem both in Frechet and in Banach spaces.

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Dorokhov, Alexander, and Michael Karpov. "On the existence of fixed points in completely continuous operators in F -space." Tambov University Reports. Series: Natural and Technical Sciences, no. 125 (2019): 26–32. http://dx.doi.org/10.20310/1810-0198-2019-24-125-26-32.

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This work is dedicated to the development of the theory of fixed points of completely continuous operators. We prove existence of new theorems of fixed points of completely continuous operators in F -space (Frechet space). This class of spaces except Banach includes such important space as a countably normed space and Lp(0 < p < 1), lp(0 < p < 1).

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Helal, Mohamed. "Fractional order differential inclusions on an unbounded domain with infinite delay." MATHEMATICA 62 (85), no. 2 (November 15, 2020): 167–78. http://dx.doi.org/10.24193/mathcluj.2020.2.06.

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We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

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Carrión, H., P. Galindo, and M. L. Lourenço. "Biholomorphic Mappings on Banach Spaces." Proceedings of the Edinburgh Mathematical Society 62, no. 4 (February 27, 2019): 913–24. http://dx.doi.org/10.1017/s0013091518000883.

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AbstractWe present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is that the derivative operator is power bounded, and which we, in turn, show to be diagonalizable in some cases, like the separable Hilbert space.

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Dissertations / Theses on the topic "Frechet derivative, Banach spaces"

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Matouskova, Eva, Charles Stegall, and stegall@bayou uni-linz ac at. "The Structure of the Frechet Derivative in Banach Spaces." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1014.ps.

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Dore, Michael J. "Universal Frechet sets in Banach spaces." Thesis, University of Warwick, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.526190.

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Chalk, Carl. "Nonlinear evolutionary equations in Banach spaces with fractional time derivative." Thesis, University of Hull, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440650.

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Hofmann, B., and O. Scherzer. "Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800957.

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The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results.

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Hofmann, B. "On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801185.

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In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed.

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Books on the topic "Frechet derivative, Banach spaces"

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Bárcenas, Noé, and Monica Moreno Rocha. Mexican mathematicians abroad: Recent contributions : first workshop, Matematicos Mexicanos Jovenes en el Mundo, August 22-24, 2012, Centro de Investigacion en Matematicas, A.C., Guanajuato, Mexico. Edited by Galaz-García Fernando editor. Providence, Rhode Island: American Mathematical Society, 2016.

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Simon, Jacques. Banach, Frechet, Hilbert and Neumann Spaces. Wiley & Sons, Incorporated, John, 2017.

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Lindenstrauss, Joram, David Preiss, and Jaroslav Tiaer. Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (Am-179). Princeton University Press, 2012.

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Advances In Ultrametric Analysis 12th International Conference On Padic Functional Analysis July 26 2012 University Of Manitoba Winnipeg Canada. American Mathematical Society, 2013.

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Book chapters on the topic "Frechet derivative, Banach spaces"

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Lindenstrauss, Joram, David Preiss, and Tiˇser Jaroslav. "Ε‎-Fr ´Echet Differentiability." In Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179). Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691153551.003.0004.

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This chapter treats results on ε‎-Fréchet differentiability of Lipschitz functions in asymptotically smooth spaces. These results are highly exceptional in the sense that they prove almost Frechet differentiability in some situations when we know that the closed convex hull of all (even almost) Fréchet derivatives may be strictly smaller than the closed convex hull of the Gâteaux derivatives. The chapter first presents a simple proof of an almost differentiability result for Lipschitz functions in asymptotically uniformly smooth spaces before discussing the notion of asymptotic uniform smoothness. It then proves that in an asymptotically smooth Banach space X, any finite set of real-valued Lipschitz functions on X has, for every ε‎ > 0, a common point of ε‎-Fréchet differentiability.

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Lindenstrauss, Joram, David Preiss, and Tiˇser Jaroslav. "Smoothness and Asymptotic Smoothness." In Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179). Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691153551.003.0008.

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This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion of spaces admitting bump functions smooth in the direction of a family of subspaces with modulus controlled by ω‎(t). It shows that this notion is related to asymptotic uniform smoothness, and that very smooth bumps, and very asymptotically uniformly smooth norms, exist in all asymptotically c₀ spaces. This allows a new approach to results on Γ‎-almost everywhere Frechet differentiability of Lipschitz functions. The chapter concludes by explaining an immediate consequence for renorming of spaces containing an asymptotically c₀ family of subspaces.

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Lindenstrauss, Joram, David Preiss, and Tiˇser Jaroslav. "Fr échet Differentiability of Real-Valued Functions." In Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179). Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691153551.003.0012.

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This chapter shows that cone-monotone functions on Asplund spaces have points of Fréchet differentiability and that the appropriate version of the mean value estimates holds. It also proves that the corresponding point of Fréchet differentiability may be found outside any given σ‎-porous set. This new result considerably strengthens known Fréchet differentiability results for real-valued Lipschitz functions on such spaces. The avoidance of σ‎-porous sets is new even in the Lipschitz case. The chapter first discusses the use of variational principles to prove Fréchet differentiability before analyzing a one-dimensional mean value problem in relation to Lipschitz functions. It shows that results on existence of points of Fréchet differentiability may be generalized to derivatives other than the Fréchet derivative.

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