Search results for "Map"

Common Fixed Points in a Partially Ordered Partial Metric Space

2013

In the first part of this paper, we prove some generalized versions of the result of Matthews in (Matthews, 1994) using different types of conditions in partially ordered partial metric spaces for dominated self-mappings or in partial metric spaces for self-mappings. In the second part, using our results, we deduce a characterization of partial metric 0-completeness in terms of fixed point theory. This result extends the Subrahmanyam characterization of metric completeness.

Fixed points for multivalued mappings in b-metric spaces

2015

In 2012, Samet et al. introduced the notion ofα-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under anα-ψ-contractive condition of Ćirić type, in the setting of completeb-metric spaces. An application to integral equation is given.

Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Kernel theorems in the setting of mixed nonquasi-analytic classes

2008

Abstract Let Ω 1 ⊂ R r and Ω 2 ⊂ R s be nonempty and open. We introduce the Beurling–Roumieu spaces D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) , D ( M , M ′ } ( Ω 1 × Ω 2 ) and obtain tensor product representations of them. This leads for instance to kernel theorems of the following type: every continuous linear map from the Beurling space D ( ω 1 ) ( Ω 1 ) (respectively D ( M ) ( Ω 1 ) ) into the strong dual of the Roumieu space D { ω 2 } ( Ω 2 ) (respectively D { M ′ } ( Ω 2 ) ) can be represented by a continuous linear functional on D ( ω 1 , ω 2 } ( Ω 1 × Ω 2 ) (respectively D ( M , M ′ } ( Ω 1 × Ω 2 ) ).

Convergence-theoretic characterizations of compactness

2002

AbstractFundamental variants of compactness are characterized in terms of concretely reflective convergence subcategories: topologies, pretopologies, paratopologies, hypotopologies and pseudotopologies. Hyperquotient maps (perfect, quasi-perfect, adherent and closed) and quotient maps (quotient, hereditarily quotient, countably biquotient, biquotient, and almost open) are characterized in terms of various degrees of compactness of their fiber relations, and of sundry relaxations of inverse continuity.

On generalized weakly G-contraction mapping in G-metric spaces

2011

In this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.

Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

2016

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we …

Lipschitz conditions,b-arcwise connectedness and conformal mappings

1982

Operators Which Do Not Have the Single Valued Extension Property

2000

Abstract In this paper we shall consider the relationships between a local version of the single valued extension property of a bounded operator T  ∈  L ( X ) on a Banach space X and some quantities associated with T which play an important role in Fredholm theory. In particular, we shall consider some conditions for which T does not have the single valued extension property at a point λ o  ∈  C .

Common fixed points for discontinuous mappings in fuzzy metric spaces

2008

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena.