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Newton's method for computation of a square root yields a difference equation which can be solved using the hyperbolic cotangent function. For the computation of the third root Newton's sequence presents a harder problem, which already Cayley was trying to solve. In the present paper two mutually inverse functions are defined in order to solve the difference equation, instead of the hyperbolic cotangent and its inverse. Several coefficients in the expansion around the fixed points are obtained,...

Discontinuous wave equations and a topological degree for some classes of multi-valued mappings

Michal Fečkan, Richard Kollár (1999)

Applications of Mathematics

The Leray-Schauder degree is extended to certain multi-valued mappings on separable Hilbert spaces with applications to the existence of weak periodic solutions of discontinuous semilinear wave equations with fixed ends.

Fixed point indices of equivariant maps and Möbius inversions.

Katsuhiro Komiya (1988)

Inventiones mathematicae

Fixed points as Nash equilibria.

Torres-Martínez, Juan Pablo (2006)

Fixed Point Theory and Applications [electronic only]

Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

The existence of multiple solutions for perturbed equations is shown near a manifold of solutions of an unperturbed equation via the Nielsen fixed point theory.

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A fixed point theorem for a class of multi-valued continuously differentiable maps

A general asymptotic fixed point theorem.

A Symplectic Fixed Point Theorem on ... .

About the attractive points of the root functions on the Riemannian foliation.

Ako riešiť algebraické rovnice pomocou rovnic diferenciálnych

An extension of the topological degree in Hilbert space.

Bifurcation of periodic orbits of time dependent Hamiltonian systems on symplectic manifolds.

Brouwer degree, equivariant maps and tensor powers.

Calcul explicite des constantes de renormalisation pour des classes particulières de fonctions unimodales

Cayley's problem

Discontinuous wave equations and a topological degree for some classes of multi-valued mappings

Fixed point indices of equivariant maps and Möbius inversions.

Fixed points as Nash equilibria.

Fixed-point free maps of Euclidean spaces

Fixed-point-like theorems on subspaces.

Homöomorphieaussagen für $k$ -verdichtende Vektorfelder

Iterates approaching hyperbolic manifolds of fixed points.

Kolmogorov problem in $W^{r} H^{ω} [0, 1]$ and extremal Zolotarev ω-splines [Book]

Minimal surface maps, fixed point indices and a Jiang-Guo type inequality

Multiple perturbed solutions near nondegenerate manifolds of solutions

Currently displaying 1 – 20 of 40

Displaying 1 – 20 of 40

Kolmogorov problem in W r H ω [ 0 , 1 ] and extremal Zolotarev ω-splines [Book]

Currently displaying 1 – 20 of 40

Kolmogorov problem in $W^{r} H^{ω} [0, 1]$ and extremal Zolotarev ω-splines [Book]