Search results for "Theorem"

Some Integral Type Fixed-Point Theorems and an Application to Systems of Functional Equations

2013

In this paper, we prove a new common fixed point theorem for four self mappings by using the notions of compatibility and subsequential continuity (alternate subcompatibility and reciprocal continuity) in metric spaces satisfying a general contractive condition of integral type. We give some examples to support the useability of our main result. Also, we obtain some fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. We conclude the paper with an application of our main result to solvability of systems of functional equations.

Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces

2011

We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.

Fixed Points for Pseudocontractive Mappings on Unbounded Domains

2010

We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and Németh. An application to integral equations is given.

Minimal nontrivial space complexity of probabilistic one- way turing machines

2005

Languages recognizable in o(log log n) space by probabilistic one — way Turing machines are proved to be regular. This solves an open problem in [4].

Metric Operators, Generalized Hermiticity and Lattices of Hilbert Spaces

2015

Pseudo-Hermitian quantum mechanics (QM) is a recent, unconventional, approach to QM, based on the use of non-self-adjoint Hamiltonians, whose self-adjointness can be restored by changing the ambient Hilbert space, via a so-called metric operator. The PT-symmetric Hamiltonians are usually pseudo-Hermitian operators, a term introduced a long time ago by Dieudonné for characterizing those bounded operators A that satisfy a relation of the form GA = A G, where G is a metric operator, that is, a strictly positive self-adjoint operator. This chapter explores further the structure of unbounded metric operators, in particular, their incidence on similarity. It examines the notion of similarity betw…

Weyl type theorems for bounded linear operators on Banach spaces

2011

In 1909 H. Weyl [59] studied the spectra of all compact linear perturbations of a self-adjoint operator defined on a Hilbert space and found that their intersection consisted precisely of those points of the spectrum where are not isolated eigenvalues of nite multiplicity. Later, the property established by Weyl for self-adjoint operators has been observed for several other classes of operators, for instance hyponormal operators on Hilbert spaces, Toeplitz operators,convolution operators on group algebras, and many other classes of operators ned on Banach spaces . In the literature, a bounded linear operator defined on a Banach space which satisfies this property is said to satisfy Weyl's t…

Some characterizations of operators satisfying a-Browder's theorem

2005

Abstract We characterize the bounded linear operators T defined on Banach spaces satisfying a-Browder's theorem, or a-Weyl's theorem, by means of the discontinuity of some maps defined on certain subsets of C . Several other characterizations are given in terms of localized SVEP, as well as by means of the quasi-nilpotent part, the hyper-kernel or the analytic core of λ I − T .

A note on the closed graph theorem

1977

On Weakly Locally Uniformly Rotund Banach Spaces

1999

Abstract We show that every normed space E with a weakly locally uniformly rotund norm has an equivalent locally uniformly rotund norm. After obtaining a σ -discrete network of the unit sphere S E for the weak topology we deduce that the space E must have a countable cover by sets of small local diameter, which in turn implies the renorming conclusion. This solves a question posed by Deville, Godefroy, Haydon, and Zizler. For a weakly uniformly rotund norm we prove that the unit sphere is always metrizable for the weak topology despite the fact that it may not have the Kadec property. Moreover, Banach spaces having a countable cover by sets of small local diameter coincide with the descript…

On Branciari’s theorem for weakly compatible mappings

2010

AbstractIn a recent paper B. Samet and H. Yazidi [B. Samet, H. Yazidi, An extension of Banach fixed point theorem for mappings satisfying a contractive condition of integral type, Ital. J. Pure Appl. Math. (in press)] have obtained an interesting theorem for mappings satisfying a contractive condition of integral type. The aim of this note is to present a generalization of their main result.