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We prove the existence of a contractive mapping on a weakly compact convex set in a Banach space that is fixed point free. This answers a long-standing open question.

A convergence theorem for Mann fixed point iteration procedure.

Rafiq, Arif (2006)

Applied Mathematics E-Notes [electronic only]

A convergent nonlinear splitting via orthogonal projection

Jan Mandel (1984)

Aplikace matematiky

We study the convergence of the iterations in a Hilbert space $V, x_{k + 1} = W (P) x_{k}, W (P) z = w = T (P w + (I - P) z)$ , where $T$ maps $V$ into itself and $P$ is a linear projection operator. The iterations converge to the unique fixed point of $T$ , if the operator $W (P)$ is continuous and the Lipschitz constant $∥(I - P) W (P)∥ < 1$ . If an operator $W (P_{1})$ satisfies these assumptions and $P_{2}$ is an orthogonal projection such that $P_{1} P_{2} = P_{2} P_{1} = P_{1}$ , then the operator $W (P_{2})$ is defined and continuous in $V$ and satisfies $∥(I - P_{2}) W (P_{2})∥ \leq ∥(I - P_{1}) W (P_{1})∥$ .

A converse to the Lions-Stampacchia theorem

Emil Ernst, Michel Théra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.

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A common fixed point theorem satisfying integral type implicit relations.

A common fixed-point theorem in 2 non-Archimedean Menger PM-space for R-weakly commuting maps of type (P).

A common unique fixed point theorem for two random operators in Hilbert spaces.

A compact evolution operator generated by a nonlinear time-dependent m-accretive operator in a Banach space.

A Construction of Stable Subharmonic Orbits in Monotone Time-periodic Dynamical Systems.

A continuation method for weakly Kannan maps.

A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals

A contractive fixed point free mapping on a weakly compact convex set

A convergence theorem for Mann fixed point iteration procedure.

A convergent nonlinear splitting via orthogonal projection

A converse to the Lions-Stampacchia theorem

A converse to the Lions-Stampacchia Theorem

A counter example on common periodic points of functions.

A counterexample to a theorem of Argyros

A counterexample to “An extension of Gregus fixed point theorem”.

A counterexample to the article “On the fixed points of affine nonexpansive mappings”.

A degree for a class of acyclic-valued vector fields in Banach spaces

A degree theory for a class of perturbed Fredholm maps.

A degree theory for a class of perturbed Fredholm maps. II.

A degree theory for compact perturbations of proper $C^{1}$ Fredholm mappings of index 0.

Currently displaying 21 – 40 of 2510