In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

We lift upper and lower estimates from linear functionals to n-homogeneous polynomials and using this result show that l ∞ is finitely represented in the space of n-homogeneous poly-nomials, n ≥ 2, for any infinite dimensional Banach space. Refinements are also given. The classical Dvoretsky spherical sections theorem [5,13] states that l 2 is finitely represented in any infinite dimensional Ba...

We study certain Banach spaces that are added in the extension by one Cohen real. Specifically, we show that adding just one Cohen real to any model adds a Banach space of density א1 which does not embed into any such space in the ground model (Theorem 1.1). Moreover, such a Banach space can be chosen to be UG (Theorem 1.6). This has consequences on the the isomorphic universality number for Ba...

in this paper, we generalize fuzzy banach contraction theorem establishedby v. gregori and a. sapena [fuzzy sets and systems 125 (2002) 245-252]using notion of altering distance which was initiated by khan et al. [bull. austral.math. soc., 30(1984), 1-9] in metric spaces.

We consider real spaces only. Definition. An operator T : X → Y between Banach spaces X and Y is called a Hahn-Banach operator if for every isometric embedding of the space X into a Banach space Z there exists a norm-preserving extension T̃ of T to Z. A geometric property of Hahn-Banach operators of finite rank acting between finite-dimensional normed spaces is found. This property is used to ch...

3 ABSTRACT. We extend a p-adic spectral theorem of M. M. Vishik to a certain class of p-adic Banach algebras. This class includes inductive limits of finite-dimensional p-Banach algebras of the form B(X), where X is a p-adic Banach space of the form X ≃ Ω p (J), J being a finite nonempty set. In particular, we present a p-adic spectral theorem for p-adic UHF algebras and p-adic TUHF algebras (T...

The famous Banach contraction principle (see, e.g., [1]) plays an important role in various fields of nonlinear analysis and applied mathematical analysis. Many authors investigated and established generalizations in various different directions of the Banach contraction principle in the past; see [1-22] and references therein. In 1969, Nadler [2] first proved a set-valued generalized version o...

In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak co...

It is proved that if a Banach space Y is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in Y has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's space is c o-saturated. §0. Introduction. We shall say that a Banach space Y has property (WU) if every normalized weakly null sequence in Y...

An extension of the Helson-Edwards theorem for the group algebras to Banach modules over commutative Banach algebras is given. This extension can be viewed as a generalization of Liu-Rooij-Wang's result for Banach modules over the group algebras.