Relevant bibliographies by topics / Fixed-point equation

Academic literature on the topic 'Fixed-point equation'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Fixed-point equation"

1

Xu, Ding, Jinglei Xu, and Gongnan Xie. "Revisiting Blasius Flow by Fixed Point Method." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/953151.

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The well-known Blasius flow is governed by a third-order nonlinear ordinary differential equation with two-point boundary value. Specially, one of the boundary conditions is asymptotically assigned on the first derivative at infinity, which is the main challenge on handling this problem. Through introducing two transformations not only for independent variable bur also for function, the difficulty originated from the semi-infinite interval and asymptotic boundary condition is overcome. The deduced nonlinear differential equation is subsequently investigated with the fixed point method, so the original complex nonlinear equation is replaced by a series of integrable linear equations. Meanwhile, in order to improve the convergence and stability of iteration procedure, a sequence of relaxation factors is introduced in the framework of fixed point method and determined by the steepest descent seeking algorithm in a convenient manner.
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Brzdęk, Janusz, Liviu Cădariu, and Krzysztof Ciepliński. "Fixed Point Theory and the Ulam Stability." Journal of Function Spaces 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/829419.

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The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.
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Sihombing, S. C., and L. Lia. "Fixed point theorem on volterra integral equation." Journal of Physics: Conference Series 1375 (November 2019): 012064. http://dx.doi.org/10.1088/1742-6596/1375/1/012064.

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4

Hammad, Hasanen A., Hassen Aydi, and Manuel De la Sen. "Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions." Complexity 2021 (February 22, 2021): 1–13. http://dx.doi.org/10.1155/2021/5730853.

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This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.
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Garakoti, Neeraj, Joshi Chandra, and Rohit Kumar. "Fixed point for F⊥-weak contraction." Mathematica Moravica 25, no. 1 (2021): 113–22. http://dx.doi.org/10.5937/matmor2101113g.

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6

Amattouch, Mohamed Ridouan, and Hassan Belhadj. "A modified fixed point method for biochemical transport." Boletim da Sociedade Paranaense de Matemática 40 (February 2, 2022): 1–5. http://dx.doi.org/10.5269/bspm.46947.

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This work is devoted to a modified fixed point method applied to the bio-chemical transport equation. To have a good accuracy for the solution we treat, we apply an implicit scheme to this equation and use a modified fixed point technique to linearize the problem of transport equation with a generalized nonlinear reaction and diffusion equation. Next, we apply this methods in particular to the the dynamical system of a bio-chemical process. Eventually, we accelerate these algorithms by the optimized domain decomposition methods.Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposednew method.
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7

Lowenthal, Franklin, Arnold Langsen, and Clark T. Benson. "Merton's Partial Differential Equation and Fixed Point Theory." American Mathematical Monthly 105, no. 5 (May 1998): 412. http://dx.doi.org/10.2307/3109802.

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Lowenthal, Franklin, Arnold Langsen, and Clark T. Benson. "Merton's Partial Differential Equation and Fixed Point Theory." American Mathematical Monthly 105, no. 5 (May 1998): 412–20. http://dx.doi.org/10.1080/00029890.1998.12004903.

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Babiarz, Artur, Jerzy Klamka, and Michał Niezabitowski. "Schauder’s fixed-point theorem in approximate controllability problems." International Journal of Applied Mathematics and Computer Science 26, no. 2 (June 1, 2016): 263–75. http://dx.doi.org/10.1515/amcs-2016-0018.

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AbstractThe main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
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Park, Choonkil, and Ji-Hye Kim. "The Stability of a Quadratic Functional Equation with the Fixed Point Alternative." Abstract and Applied Analysis 2009 (2009): 1–11. http://dx.doi.org/10.1155/2009/907167.

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Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.
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Dissertations / Theses on the topic "Fixed-point equation"

1

Dunn, Kyle George. "An Integral Equation Method for Solving Second-Order Viscoelastic Cell Motility Models." Digital WPI, 2014. https://digitalcommons.wpi.edu/etd-theses/578.

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For years, researchers have studied the movement of cells and mathematicians have attempted to model the movement of the cell using various methods. This work is an extension of the work done by Zheltukhin and Lui (2011), Mathematical Biosciences 229:30-40, who simulated the stress and displacement of a one-dimensional cell using a model based on viscoelastic theory. The report is divided into three main parts. The first part considers viscoelastic models with a first-order constitutive equation and uses the standard linear model as an example. The second part extends the results of the first to models with second-order constitutive equations. In this part, the two examples studied are Burger model and a Kelvin-Voigt element connected with a dashpot in series. In the third part, the effects of substrate with variable stiffness are explored. Here, the effective adhesion coefficient is changed from a constant to a spatially-dependent function. Numerical results are generated using two different functions for the adhesion coefficient. Results of this thesis show that stress on the cell varies greatly across each part of the cell depending on the constitute equation we use, while the position and velocity of the cell remain essentially unchanged from a large-scale point of view.
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Kang, Jinghong. "The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30435.

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This thesis deals with non-linear non-quadratic optimal control problems in an autonomous system and a related iterative numerical method, the Kleinman-Newton method, for solving the problem. The thesis proves the local convergence of Kleinman-Newton method using the contraction mapping theorem and then describes how this Kleinman-Newton method may be used to numerically solve for the optimal control and the corresponding solution. In order to show the proof and the related numerical work, it is necessary to review some of earlier work in the beginning of Chapter 1 [Zhang], and to introduce the Kleinman-Newton method at the end of the chapter. In Chapter 2 we will demonstrate the proof. In Chapter 3 we will show the related numerical work and results.
Ph. D.
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3

Ertem, Turker. "Asymptotic Integration Of Dynamical Systems." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615405/index.pdf.

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In almost all works in the literature there are several results showing asymptotic relationships between the solutions of x&prime
&prime
= f (t, x) (0.1) and the solutions 1 and t of x&prime
&prime
= 0. More specifically, the existence of a solution of (0.1) asymptotic to x(t) = at + b, a, b &isin
R has been obtained. In this thesis we investigate in a systematic way the asymptotic behavior as t &rarr
&infin
of solutions of a class of differential equations of the form (p(t)x&prime
)&prime
+ q(t)x = f (t, x), t &ge
t_0 (0.2) and (p(t)x&prime
)&prime
+ q(t)x = g(t, x, x&prime
), t &ge
t_0 (0.3) by the help of principal u(t) and nonprincipal v(t) solutions of the corresponding homogeneous equation (p(t)x&prime
)&prime
+ q(t)x = 0, t &ge
t_0. (0.4) Here, t_0 &ge
0 is a real number, p &isin
C([t_0,&infin
), (0,&infin
)), q &isin
C([t_0,&infin
),R), f &isin
C([t_0,&infin
) ×
R,R) and g &isin
C([t0,&infin
) ×
R ×
R,R). Our argument is based on the idea of writing the solution of x&prime
&prime
= 0 in terms of principal and nonprincipal solutions as x(t) = av(t) + bu(t), where v(t) = t and u(t) = 1. In the proofs, Banach and Schauder&rsquo
s fixed point theorems are used. The compactness of the operator is obtained by employing the compactness criteria of Riesz and Avramescu. The thesis consists of three chapters. Chapter 1 is introductory and provides statement of the problem, literature review, and basic definitions and theorems. In Chapter 2 first we deal with some asymptotic relationships between the solutions of (0.2) and the principal u(t) and nonprincipal v(t) solutions of (0.4). Then we present existence of a monotone positive solution of (0.3) with prescribed asimptotic behavior. In Chapter 3 we introduce the existence of solution of a singular boundary value problem to the Equation (0.2).
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Čambor, Michal. "Paralelní řešení parciálních diferenciálnich rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-412855.

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This thesis deals with the concepts of numerical integrator using floating point arithmetic for solving partial differential equations. The integrator uses Euler method and Taylor series. Thesis shows parallel and serial approach to computing with exponents and significands. There is also a comparison between modern parallel systems and the proposed concepts.
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Rocha, Suelen de Souza. "Soluções clássicas para uma equação elíptica semilinear não homogênea." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/8051.

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Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-29T13:33:49Z No. of bitstreams: 1 arquivo total.pdf: 5320246 bytes, checksum: 158dd460a20ce46c96d4a34623612264 (MD5)
Made available in DSpace on 2016-03-29T13:33:49Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 5320246 bytes, checksum: 158dd460a20ce46c96d4a34623612264 (MD5) Previous issue date: 2011-08-25
This work is mainly concerned with the existence and nonexistence of classical solution to the nonhomogeneous semilinear equation Δu + up + f(x) = 0 in Rn, u > 0 in Rn, when n 3, where f 0 is a Hölder continuous function. The nonexistence of classical solution is established when 1 < p n=(n 􀀀 2). For p > n=(n 􀀀 2) there may be both existence and nonexistence results depending on the asymptotic behavior of f at infinity. The existence results were obtained by employed sub and supersolutions techniques and fixed point theorem. For the nonexistence of classical solution we used a priori integral estimates obtained via averaging.
Neste trabalho, estamos interessados na existência e não existência de solução clássica para a equação não homogênea semilinear Δu + up + f(x) = 0 em Rn; u > 0 em Rn, n 3 onde f 0 é uma função Hölder contínua. A não existência de solução clássica é estabelecida quando 1 < p n=(n 􀀀 2). Para p > n=(n 􀀀 2), temos resultados de existência e não existência de solução clássica, dependendo do comportamento assin- tótico de f no infinito. Os resultados de existência foram obtidos usando o método de sub e supersolução e teoremas de ponto fixo. A não existência de solução clássica é obtida usando-se estimativas integrais a priori via média esférica.
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6

Rizzolo, Douglas. "Approximating Solutions to Differential Equations via Fixed Point Theory." Scholarship @ Claremont, 2008. https://scholarship.claremont.edu/hmc_theses/213.

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In the study of differential equations there are two fundamental questions: is there a solution? and what is it? One of the most elegant ways to prove that an equation has a solution is to pose it as a fixed point problem, that is, to find a function f such that x is a solution if and only if f (x) = x. Results from fixed point theory can then be employed to show that f has a fixed point. However, the results of fixed point theory are often nonconstructive: they guarantee that a fixed point exists but do not help in finding the fixed point. Thus these methods tend to answer the first question, but not the second. One such result is Schauder’s fixed point theorem. This theorem is broadly applicable in proving the existence of solutions to differential equations, including the Navier-Stokes equations under certain conditions. Recently a semi-constructive proof of Schauder’s theorem was developed in Rizzolo and Su (2007). In this thesis we go through the construction in detail and show how it can be used to search for multiple solutions. We then apply the method to a selection of differential equations.
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7

Sun, Xun. "Twin solutions of even order boundary value problems for ordinary differential equations and finite difference equations." [Huntington, WV : Marshall University Libraries], 2009. http://www.marshall.edu/etd/descript.asp?ref=1014.

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8

Mentemeier, Sebastian [Verfasser], and Gerold [Akademischer Betreuer] Alsmeyer. "On multivariate stochastic fixed point equations / Sebastian Mentemeier. Betreuer: Gerold Alsmeyer." Münster : Universitäts- und Landesbibliothek der Westfälischen Wilhelms-Universität, 2013. http://d-nb.info/1031885455/34.

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9

Cremins, Casey Timothy. "Fixed point indices and existence theorems for semilinear equations in cones." Thesis, University of Glasgow, 1997. http://theses.gla.ac.uk/3520/.

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The purpose of this thesis is to develop fixed point indices for A-proper semilinear operators defined on cones in Banach spaces and use the results to obtain existence theorems to semilinear equations. We consider semilinear equations of the form Lx = Nx where L is a linear Fredholm operation of index zero, N a nonlinear operator such that L - N is A-proper at zero relative to a projection scheme L. Chapter 1 is an introduction to basic concepts used throughout the thesis, including; Banach spaces, linear operators, A-proper maps, Fredholm operators of index zero, and the definition and properties of the generalised degree for A-proper maps. In Chapter 2, we define a fixed point index for A-proper maps on cones in terms of the generalised degree and derive the basic properties of this index. We then extend the definition to include unbounded sets. A more general fixed point index than that of Chapter 2 is developed in Chapter 3 for A-proper maps based on limits of a finite dimensionally defined index. Properties of the index are given and a definition for unbounded sets is provided. Chapter 4 extends the Lan-Webb fixed point index for weakly inward A-proper at 0 maps to semilinear operators. This index is also extended to include unbounded sets. Existence theorems of positive and non-negative solutions to semilinear equations on cones are established in Chapter 5 using the fixed point indices of Chapters 2, 3, and 4. Finally, in Chapter 6, we apply some of the existence theorems of Chapter 5 to several differential and integral equations. We prove the existence of: a positive solution to a Picard boundary value problem; a non-negative solution to a periodic boundary value problem; and, a non-negative solution to a Volterra integral equation.
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Tiwari, Abhishek. "ANALYTICAL METHODS FOR TRANSPORT EQUATIONS IN SIMILARITY FORM." UKnowledge, 2007. http://uknowledge.uky.edu/gradschool_theses/457.

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We present a novel approach for deriving analytical solutions to transport equations expressedin similarity variables. We apply a fixed-point iteration procedure to these transformedequations by formally solving for the highest derivative term and then integrating to obtainan expression for the solution in terms of a previous estimate. We are able to analyticallyobtain the Lipschitz condition for this iteration procedure and, from this (via requirements forconvergence given by the contraction mapping principle), deduce a range of values for the outerlimit of the solution domain, for which the fixed-point iteration is guaranteed to converge.
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Books on the topic "Fixed-point equation"

1

The heat kernel Lefschetz fixed point formula for the spin-c dirac operator. Boston: Birkhauser, 1996.

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Johnny, Henderson, and Ouahab Abdelghani, eds. Impulsive differential inclusions: A fixed point approach. Berlin: Walter de Gruyter GmbH & Co., KG, 2013.

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Point estimation of root finding methods. [New York]: Springer, 2008.

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Multivalued differential equations. Berlin: W. de Gruyter, 1992.

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Fixed-point algorithms for inverse problems in science and engineering. New York: Springer, 2011.

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Points fixes, points critiques et problèmes aux limites. Montréal, Québec, Canada: Presses de l'Université de Montréal, 1985.

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Seppo, Heikkilä, ed. Fixed point theory in ordered sets and applications: From differential and integral equations to game theory. New York, NY: Springer, 2011.

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1926-, Lakshmikantham V., ed. Nonlinear problems in abstract cones. Boston: Academic Press, 1988.

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Zur Existenz klassischer Lösungen einer elliptischen Differentialgleichung zweiter Ordnung. Warszawa: Państwowe Wydawn. Naukowe, 1987.

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Yang, Zaifu. Computing equilibria and fixed points: The solution of nonlinear inequalities. Boston, Mass: Kluwer Academic, 1999.

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Book chapters on the topic "Fixed-point equation"

1

Csató, Gyula, Bernard Dacorogna, and Olivier Kneuss. "An Abstract Fixed Point Theorem." In The Pullback Equation for Differential Forms, 413–16. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8313-9_18.

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Almahalebi, M., A. Charifi, S. Kabbaj, and E. Elqorachi. "A Fixed Point Approach to Stability of the Quadratic Equation." In Topics in Mathematical Analysis and Applications, 53–77. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06554-0_3.

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Keller, Wolfgang. "Solving the STEP-Observation Equation Using Banach’s Fixed-Point Principle." In International Association of Geodesy Symposia, 117–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79721-7_14.

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Melliani, S., M. Elomari, and L. S. Chadli. "Solving Generalized Fractional Schrodinger’s Equation by Mean Generalized Fixed Point." In Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications, 83–102. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26149-8_7.

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Elhoucien, Elqorachi, and Manar Youssef. "Fixed Point Approach to the Stability of the Quadratic Functional Equation." In Springer Optimization and Its Applications, 259–77. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3498-6_14.

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Jung, Soon-Mo. "Fixed Point Approach to the Stability of the Gamma Functional Equation." In Springer Optimization and Its Applications, 353–61. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3498-6_21.

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Kenary, Hassan Azadi. "Random Stability of an AQCQ Functional Equation: A Fixed Point Approach." In Springer Optimization and Its Applications, 363–80. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3498-6_22.

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Park, Choonkil, and Themistocles M. Rassias. "Fuzzy Stability of an Additive-Quartic Functional Equation: A Fixed Point Approach." In Functional Equations in Mathematical Analysis, 247–60. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0055-4_20.

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Cădariu, Liviu, and Viorel Radu. "A General Fixed Point Method for the Stability of Cauchy Functional Equation." In Functional Equations in Mathematical Analysis, 19–32. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0055-4_3.

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Jung, Soon-Mo, and Themistocles M. Rassias. "A Fixed Point Approach to the Stability of a Logarithmic Functional Equation." In Nonlinear Analysis and Variational Problems, 99–109. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0158-3_9.

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Conference papers on the topic "Fixed-point equation"

1

Melliani, Said, Abdellah Taqbibt, M. Chaib, and Lalla Saadia Chadli. "Solving Generalized Heat Equation by Mean Generalized Fixed Point." In 2020 IEEE 6th International Conference on Optimization and Applications (ICOA). IEEE, 2020. http://dx.doi.org/10.1109/icoa49421.2020.9094512.

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Qu, Liangdong, and Dengxu He. "Solving fixed point equation by niche particle swarm optimization." In 2010 2nd International Conference on Future Computer and Communication. IEEE, 2010. http://dx.doi.org/10.1109/icfcc.2010.5497677.

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Klamka, Jerzy. "Controllability problem of neutral equation with Nussbaum fixed-point theorem." In 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR). IEEE, 2016. http://dx.doi.org/10.1109/mmar.2016.7575186.

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Chen, Weijie, Chenglin Wen, and Yi Ren. "Multi-Dimensional Observation Characteristic Function Filtering Based On Fixed Point Equation." In 2018 International Conference on Control, Automation and Information Sciences (ICCAIS). IEEE, 2018. http://dx.doi.org/10.1109/iccais.2018.8570557.

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Shevchenko, Igor V. "The Fixed Point Iteration and Newton’s Methods for the Nonlinear Wave Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990968.

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Varga, Arpad, Levente Kovacs, Gyorgy Eigner, Dusan Kocur, and Jozsef K. Tar. "Fixed Point Iteration-based Adaptive Control for a Delayed Differential Equation Model of Diabetes Mellitus." In 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC). IEEE, 2019. http://dx.doi.org/10.1109/smc.2019.8914617.

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Peikert, Vincent, and Andreas Schenk. "A first analysis of a new fixed point iteration of the Boltzmann equation: Application to TCAD." In 2009 Ph.D. Research in Microelectronics and Electronics (PRIME). IEEE, 2009. http://dx.doi.org/10.1109/rme.2009.5201351.

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Xing, Gaofeng, Lingling Zhang, and Xin Zhao. "Fixed point results based on set $P_{h,e}$ and application in nonlinear fractional differential equation." In 2021 33rd Chinese Control and Decision Conference (CCDC). IEEE, 2021. http://dx.doi.org/10.1109/ccdc52312.2021.9601401.

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Berti, Massimiliano. "Nonlinear vibrations of completely resonant wave equations." In Fixed Point Theory and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc77-0-4.

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KODZHA, MEHMED. "ON THE CAUCHY PROBLEM FOR THE STRONG DISPERSIVE NONLINEARWAVE EQUATION." In INTERNATIONAL SCIENTIFIC CONFERENCE MATHTECH 2022. Konstantin Preslavsky University Press, 2022. http://dx.doi.org/10.46687/gmkw7508.

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In this paper we consider the Cauchy problem for the strong dispersive nonlinear wave equation. We proof that the operator of the linearization arround the self-similar solutions generate C0-semigroup in Sobolev space Hs. Global existence is obtained via Banach fixed point theorem.
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Reports on the topic "Fixed-point equation"

1

Laos, Hector. Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed. Office of Scientific and Technical Information (OSTI), April 2020. http://dx.doi.org/10.2172/1649228.

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