Sentence examples for mapping principle for from inspiring English sources

We start by presenting one of the most interesting generalizations of Banach's contraction mapping principle for mappings T : X k → X, obtained in 1965 by Prešić [20], which will be fundamental in establishing our stability results for k-step fixed point iterative methods in the present paper.

Ran and Reurings [22] proved the analog of the Banach contraction mapping principle for continuous self-mappings under certain conditions in the context of a partially ordered set.

Recently, Niculescu and Roventa established the KKM mapping principle for CAT 0) spaces [11].

Therefore, by the contraction mapping principle, for given v ∈ V, there exists a unique z = ( I − P ) L 2 which satisfies (2.6).

Darbo [2], using this measure, generalized both the classical Schauder fixed point principle and (a special variant of) Banach's contraction mapping principle for so called condensing operators.

Therefore, by the contraction mapping principle, for each given (Yin V), (i=1, 2,ldots, n), there exists a unique (z_{i}in I-P L^{2}(Omega,R)) which satisfies (2.11).

Of course, the Banach contraction mapping principle [1] is the first important result on fixed points for contractive-type mappings.

(Banach contraction mapping principle [6]).

Section 3 is devoted to reviewing Krasnoselkii's fixed point theorem, Schauder type fixed point theorem, Banach's contraction mapping principle and nonlinear alternative for single-valued maps and to applying them to analyze the problem in order to show the main results.

Based on a basic property of the p-Laplacian operator and the Banach contraction mapping principle, the uniqueness of solutions for the fractional order differential equation is established for the cases p > 2 and 1 < p ≤ 2. MSC:26A34B104B10.

It is obvious that the conditions for contraction mapping principle are too strong.