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In this paper several fixed point theorems for a class of mappings defined on a complete G-metric space are proved. In the same time we show that if the G-metric space (X, G) is symmetric then the existence and uniqueness of these fixed point results follows from the Hardy-Rogers theorem in the induced usual metric space (X, d G). We also prove fixed point results for mapping on a G-metric space (X, G) by using the Hardy-Rogers theorem where (X, G) need not be symmetric.
References [1] ABBAS , M . AND RHOADES , B. E . Fixed and periodic point results in cone metric space . Appl. Math. Lett . 2 ( 2009 ), 511 – 515 . [2] AÇIK DEMIRCI I . AND GÜRDAL , M . On generalized statistical convergence via ideal in
Abstract
We give a new and simple proof to show that no homeomorphism of infinite compact metric spaces is positively expansive.
Abstract
We establish relationships between locally compact-metric spaces and all kinds of spaces with mk-system (compact k-network) by means of compact-covering mappings, quotient mapping and closed mappings.
Abstract
We study the hyperbolicity of metric spaces in the Gromov sense. We deduce the hyperbolicity of a space from the hyperbolicity of its “building block components”. These results are valuable since they simplify notably the topology of the space and allow to obtain global results from local information. We also study how the punctures and the decomposition of a Riemann surface in Y-pieces and funnels affect the hyperbolicity of the surface.
Summary
A pretopology on a given set can be generated from a filter of reflexive relations on that set (we call such a structure a preuniformity). We show that the familly of filters inducing a given pretopology on Xform a complete lattice in the lattice of filters on X. The smallest and largest elements of that lattice are explicitly given. The largest element is characterized by a condition which is formally equivalent to a property introduced by Knaster--Kuratowski--Mazurkiewicz in their well known proof of Brouwer's fixed point theorem. Menger spaces and probabilistic metric spaces also generate pretopologies. Semi-uniformities and pretopologies associated to a possibly nonseparated Menger space are completely characterized.
In this paper, we prove that a space X is a weak-open compact image of a locally separable metric space if and only if X has a uniform cosmic-weak-base if and only if X is a weak-open compact image of a metric space and a locally cosmic space, and give some internal characterizations of weak-open s-images of locally separable metric spaces.
A decomposition theorem about closed images of locally compact metric spaces is discussed. It is shown that a space is a closed image of a locally compact metric space if and only if it is a regular Fréchet space with a point-countable k-network, and each of its closed first-countable subset is locally compact.
In this paper, we give a characterization of compact-valued continuous relations on metric spaces. By this characterization, we prove that for two relations f and g on a metric space X , the composition gf of f with g is compact-valued continuous if both f and g are compact-valued continuous. As a corollary of this result, for a relation f on a metric space X , f n is a compact-valued continuous for all n ∈ ℕ iff f is a compact-valued continuous, which improves a result of H. Y. Chu and J. S. Park by omitting locally compactness of X .
Abstract
We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper.
