New extension of the Banach contraction principle to locally convex spaces and applications

Banach Envelopes of Non-locally Convex Spaces

Then Xc is the completion of {X, \\ \\c). Alternatively || ||c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X —> Z into a Banach space extends with preservation of norm to an operator L\XC —» Z. The Banach envelope of / (0 < p < 1) is, of course, lx. In 1969, Duren, Romberg and Shields [3] identified the dual space of H_...

Structure of Local Banach Spaces of Locally Convex Spaces

1. Introduction and notation. In this paper the word " local " is used in at least three different meanings. Our aim is to study local Banach spaces of Fréchet or other locally convex spaces, and it turns out that it is convenient to use the local theory of Banach spaces for this purpose. Recall that given a locally convex space E and a continuous seminorm p on E the completion of the normed sp...

Locally Uniformly Convex Norms in Banach Spaces and Their Duals

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.

Banach Algebras of Operators on Locally Convex Spaces

Banach contraction principle for cyclical mappings on partial metric spaces

*Correspondence: [email protected] 1Department of Mathematics, Çankaya University, Ankara, 06530, Turkey Full list of author information is available at the end of the article Abstract We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (I...