Search results for "metric space."
showing 10 items of 310 documents
Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces
2014
Abstract Let X be a non-empty set. We say that an element x ∈ X is a φ-fixed point of T, where φ : X → [ 0 , ∞ ) and T : X → X , if x is a fixed point of T and φ ( x ) = 0 . In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p. MSC:54H25, 47H10.
On a pair of fuzzy $\varphi$-contractive mappings
2010
We establish common fixed point theorems for fuzzy mappings under a $\varphi$-contraction condition on a metric space with the d_$\infty$-metric (induced by the Hausdorff metric) on the family of fuzzy sets. The study of fixed points of fuzzy set-valued mappings related to the d_$\infty$-metric is useful in geometric problems arising in high energy physics. Our results generalize some recent results.
A Structural Theorem for Metric Space Valued Mappings of Φ-bounded Variation
2009
In this paper we introduce the notion of $\Phi$-bounded variation for metric space valued mappings defined on a subset of the real line. Such a notion generalizes the one for real functions introduced by M. Schramm, and many previous generalized variations. We prove a structural theorem for mappings of $\Phi$-bounded variation. As an application we show that each mapping of $\Phi$-bounded variation defined on a subset of $\mathbb{R}$ possesses a $\Phi$-variation preserving extension to the whole real line.
A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces
2013
Abstract In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming.
JH-Operators and Occasionally Weakly g-Biased Pairs in Fuzzy Symmetric Spaces
2013
We introduce the notions of $\mathcal{JH}$-operators and occasionally weakly $g$-biased mappings in fuzzy symmetric spaces to prove common fixed point theorems for self-mappings satisfying a generalized mixed contractive condition. We also prove analogous results for two pairs of $\mathcal{JH}$-operators by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. We give also an application of our results to product spaces.
Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation
2013
We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
A fixed point theorem inG-metric spaces viaα-series
2014
In the context of G -metric spaces we prove a common fixed point theorem for a sequence of self mappings using a new concept of α-series. Keywords: α-series, common fixed point, G -metric space Quaestiones Mathematicae 37(2014), 429-434
A property of connected Baire spaces
1997
Abstract We give a topological version of a classical result of F. Sunyer Balaguer's on a local characterization of real polynomials. This is done by studying a certain property on a class of connected Baire spaces, thus allowing us to obtain a local characterization of repeated integrals of analytic maps on Banach spaces.
Best Proximity Point Results in Non-Archimedean Fuzzy Metric Spaces
2013
We consider the problem of finding a best proximity point which achieves the minimum distance between two nonempty sets in a non-Archimedean fuzzy metric space. First we prove the existence and uniqueness of the best proximity point by using di fferent contractive conditions, then we present some examples to support our best proximity point theorems.
Finitely randomized dyadic systems and BMO on metric measure spaces
2015
Abstract We study the connection between BMO and dyadic BMO in metric measure spaces using finitely randomized dyadic systems, and give a Garnett–Jones type proof for a theorem of Uchiyama on a construction of certain BMO functions. We obtain a relation between the BMO norm of a suitable expectation over dyadic systems and the dyadic BMO norms of the original functions in different systems. The expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions. Applying our result, we derive Uchiyama’s theorem from its dyadic counterpart, which we also prove.