Search results for "contractive mapping"
showing 10 items of 16 documents
Some new fixed point results in non-Archimedean fuzzy metric spaces
2013
In this paper, we introduce the notions of fuzzy $(\alpha,\beta,\varphi)$-contractive mapping, fuzzy $\alpha$-$\phi$-$\psi$-contractive mapping and fuzzy $\alpha$-$\beta$-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results.
Fixed points in weak non-Archimedean fuzzy metric spaces
2011
Mihet [Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008) 739-744] proved a theorem which assures the existence of a fixed point for fuzzy $\psi$-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.
Further generalization of fixed point theorems in Menger PM-spaces
2015
In this work, we establish some fixed point theorems by revisiting the notion of ψ-contractive mapping in Menger PM-spaces. One of our results (namely, Theorem 2.3) may be viewed as a possible answer to the problem of existence of a fixed point for generalized type contractive mappings in M-complete Menger PM-spaces under arbitrary t-norm. Some examples are furnished to demonstrate the validity of the obtained results.
Fixed point theorems for $\alpha$-$\psi$-contractive type mappings
2012
In this paper, we introduce a new concept of $\alpha$-$\psi$-contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
Some new fixed point theorems in fuzzy metric spaces
2014
Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of alpha-phi -fuzzy contractive mapping and beta-psi-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.
Fixed point results for $GP_(Λ,Θ)$-contractive mappings
2014
In this paper, we introduce new notions of GP-metric space and $GP_(Λ,Θ)$-contractive mapping and then prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach contraction principle to GP-metric spaces. An example shows the usefulness of our results.
On approximating curves associated with nonexpansive mappings
2011
Let X be a Banach space with metric d. Let T, N : X → X be a strict d-contraction and a d-nonexpansive map, respectively. In this paper we investigate the properties of the approximating curve associated with T and N. Moreover, following [3], we consider the approximating curve associated with a holomorphic map f : B → α B and a ρ-nonexpansive map M : B → B, where B is the open unit ball of a complex Hilbert space H, ρ is the hyperbolic metric defined on B and 0 ≤ α < 1. We give conditions on f and M for this curve to be injective, and we show that this curve is continuous.
Fixed point results for $r$-$(\mathbf{\eta},\xi,\psi)$-contractive mappings of type (I), (II) and (III)
2013
In this paper, we introduce some classes of $r$-$(\eta,\xi,\psi)$-contractive mappings and prove results of fixed point in the setting of complete metric spaces. Some examples and an application to integral equations are given to illustrate the usability of the obtained results.
Fixed points for weak alpha-psi-contractions in partial metric spaces
2013
Recently, Samet et al. (2012) introduced the notion of $\alpha $ - $\psi $ -contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak $\alpha $ - $\psi $ -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.
A New Approach of Some Contractive Mappings on Metric Spaces
2021
In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated.