Sentence examples for mappings associated to from inspiring English sources

A set of interpolating mappings associated to a cubic spline is defined and the density of fractal cubic splines in is proven.

In this section, we investigate the stability problem for -linear mappings associated to the functional inequality (1.2) on a restricted domain.

As an application, we give an investigation of the convergence and stability of some iterative processes associated to these mappings.

The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of nonexpansive mappings and for Banach spaces associated to a locally compact group.

When n = d and Φ ( y ) = P ( | y | ) y ′ with P ( y ) being a real polynomial on ℝ satisfying P ( 0 ) = 0, Wu [12] proved that μ Ω Φ is bounded on L p ( R n ) for 1 + 1 / ( 2 β ) < p < 1 + 2 β provided that Ω ∈ F β ( S n − 1 ) for some β > 1 / 2. The L p boundedness for the Marcinkiewicz integral operator associated to polynomial mappings has also been obtained (see [6, 13]).

The same point applies to the mappings associated with each of the other three boxes.

It is worth mentioning that the results established for total asymptotically nonexpansive mappings are applicable to the mappings associated with the class of asymptotically nonexpansive mappings and which are extensions of nonexpansive mappings.

The paper is organized as follows: in Section 2 we summarize some fixed point theorems for mappings satisfying Prešić type contractive conditions, in Section 3 we present the basic concepts and results concerning the stability of fixed point iteration procedures associated to self-mappings that satisfy explicit contractive conditions.

Then the matrices associated to the linear mappings are − D 0, − A 0 (see below).

Then the matrices associated to the linear mappings are − B 1, − C 1 (see below).

The idea of the definition of a total asymptotically nonexpansive mappings is to unify various definitions of classes of mappings associated with the class of asymptotically nonexpansive mappings and to prove a general convergence theorems applicable to all these classes of nonlinear mappings.