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Factorization and extension of positive homogeneous polynomials

Andreas Defant, Mieczysław Mastyło (2014)

Studia Mathematica

We study the following problem: Given a homogeneous polynomial from a sublattice of a Banach lattice to a Banach lattice, under which additional hypotheses does this polynomial factorize through L p -spaces involving multiplication operators? We prove that under some lattice convexity and concavity hypotheses, for polynomials certain vector-valued norm inequalities and weighted norm inequalities are equivalent. We combine these results and prove a factorization theorem for positive homogeneous polynomials...

Factorizing multilinear operators on Banach spaces, C*-algebras and JB*-triples

Carlos Palazuelos, Antonio M. Peralta, Ignacio Villanueva (2009)

Studia Mathematica

In recent papers, the Right and the Strong* topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong*-to-norm continuity of a multilinear operator T defined on C*-algebras (respectively, JB*-triples) to C*-summability (respectively, JB*-triple-summability)....

Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L 1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L 1 and L ∞ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L 1 convergence without any convergence rate....

Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L1 and L∞, respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L1 convergence without any...

Firmly pseudo-contractive mappings and fixed points

Birendra Kumar Sharma, Daya Ram Sahu (1997)

Commentationes Mathematicae Universitatis Carolinae

We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.

Fixed and coincidence points of hybrid mappings

H. K. Pathak, M. S. Khan (2002)

Archivum Mathematicum

The purpose of this note is to provide a substantial improvement and appreciable generalizations of recent results of Beg and Azam; Pathak, Kang and Cho; Shiau, Tan and Wong; Singh and Mishra.

Fixed point and continuation results for contractions in metric and gauge spaces

M. Frigon (2007)

Banach Center Publications

We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

Kanokwan Sawangsup, Wutiphol Sintunavarat (2017)

Open Mathematics

The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation....

Fixed point approximation under Mann iteration beyond Ishikawa

Anthony Hester, Claudio H. Morales (2020)

Commentationes Mathematicae Universitatis Carolinae

Consider the Mann iteration x n + 1 = ( 1 - α n ) x n + α n T x n for a nonexpansive mapping T : K → K defined on some subset K of the normed space X . We present an innovative proof of the Ishikawa almost fixed point principle for nonexpansive mapping that reveals deeper aspects of the behavior of the process. This fact allows us, among other results, to derive convergence of the process under the assumption of existence of an accumulation point of { x n } .

Fixed point free maps of a closed ball with small measures of noncompactness.

Martin Väth (2001)

Collectanea Mathematica

We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.

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