Results 201 to 210 of about 4,748 (237)

Some Fixed Point Theorems in Metric and Banach Spaces

Canadian Mathematical Bulletin, 1969
The purpose of this paper is two-fold. Sections 2 and 3 are motivated by an observation that certain theorems concerning "diminishing orbital diameters" (introduced in [1]) are true under weaker assumptions. Specifically, we investigate the relationship between that concept and alternate conditions such as "asymptotic regularity", and in the process we
Belluce, L. P., Kirk, W. A.
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Banach's Fixed-Point Theorem as a base for data-type equations

Applied Categorical Structures, 1994
The paper develops a theory of data types in categories enriched by CMS (complete metric spaces) analogous to the theory in categories enriched by CPO (complete posets). In this case for a category \({\mathcal K}\) of data types solutions of recursive data-type equations \(X\cong T(X)\), where \(T:{\mathcal K}\to{\mathcal K}\) is a locally continuous ...
Jirí Adámek, Jan Reiterman
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Fixed point theorem for -nonexpansive mappings in Banach spaces

Nonlinear Analysis: Theory, Methods & Applications, 2011
The concept of \(\alpha\)-nonexpansive mapping in a Banach space is introduced and some generalizations of previous theorems from Hilbert to Banach spaces are given. Definition. Let \(E\) be a Banach space and \(C\subset E\).
Aoyama, Koji, Kohsaka, Fumiaki
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The Banach Fixed Point Theorem

2013
This chapter is devoted to the Banach fixed point theorem and some of its immediate consequences. In particular, we shall prove the usual version of the implicit function theorem in Banach spaces and present some applications to boundary value problems. This requires knowing the basic notions of differentiation in Banach spaces, which, for the reader’s
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A Novel Application of the Classical Banach Fixed Point Theorem

International Journal of Applied and Computational Mathematics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Banach Contraction Fixed Point Theorem

2018
The main goal of this chapter is to introduce notion of distance between two points in an abstract set. This concept was studied by M. Frechet and it is known as metric. Existence of a fixed point of a mapping on a complete metric into itself was proved by S. Banach around 1920.
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On a probabilistic generalization of Banach's fixed point theorem

1977
Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 31 (1977), s. 49-53 ; streszcz. pol., ros. ; Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 31 (1977), s. 49-53 ; streszcz. pol., ros.
Franke, Martin, Szynal, Dominik (1937- )
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Banach Spaces and Fixed-Point Theorems

1995
In a Banach space, the so-called norm $$ \parallel u\parallel = nonnegativenumber \hfill \\ $$ is assigned to each element u. This generalizes the absolute value |u of a real number u. The norm can be used in order to define the convergence $$ \mathop {\lim }\limits_{n \to \infty } {u_n} = u \hfill \\ $$ by means of $$ \mathop {\lim ...
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The Banach Fixed Point Theorem. The Concept of Banach Space

1998
As the proper setting for the convergence theorems of subsequent §§, we introduce the concept of a Banach space as a complete normed vector space. The Banach fixed point theorem is discussed in detail.
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Approximate Fixed Point Theorems in Banach Spaces

2016
Let \(\Omega \) be a nonempty convex subset of a topological vector space X. An approximate fixed point sequence for a map \(F: \Omega \longrightarrow \overline{\Omega }\) is a sequence \(\{x_{n}\}_{n} \in \Omega \) so that \(x_{n} - F(x_{n})\longrightarrow \theta\). Similarly, we can define approximate fixed point nets for F. Let us mention that F has
Afif Ben Amar, Donal O’Regan
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