Contractive Iterate Research Articles

A fixed point theorem for Proinov mappings with a contractive iterate

A fixed point theorem for Proinov mappings with a contractive iterate

Fixed point theorems for mappings with a contractive iterate at a point in modular metric spaces

Fixed point theorems for mappings with a contractive iterate at a point in modular metric spaces

Convergence of inexact iterates of strict contractions in metric spaces with graphs

Convergence of inexact iterates of strict contractions in metric spaces with graphs

A fixed point theorem for mappings with an F-contractive iterate

In this paper, we introduce the notion of $F$-contraction in the setting of complete metric space and we prove a fixed point theorem for $F$-contractive iteration.

A Fixed Point Result with a Contractive Iterate at a Point

In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last, the iteration number may vary for each point in the domain of the operator for which we look for a fixed point. Consequently, the proved results generalize the acknowledged results in the field, including the well-known theorems of Seghal, Kincses-Totik, and Banach-Caccioppoli. We present two illustrative examples to support our results. As an application, we consider an Ulam-stability of one of our results.

On fixed point results for Matkowski type of mappings in G-metric spaces

The main result of this paper is a fixed point theorem for Matkowski type mapping with contractive iterate at a point in a class of G-metric spaces. Our result unifies, generalizes and complements some well known results in metric and G-metric spaces.

Fixed points for mappings with a contractive iterate at each point

Abstract We generalize the results of Sehgal and Guseman for mappings on a complete metric space with a contractive iterate condition at each point.

Fixed points of mappings with a contractive iterate at a point in partial metric spaces

Abstract In 1994, Matthews introduced and studied the concept of partial metric space and obtained a Banach-type fixed point theorem on complete partial metric spaces. In this paper we study fixed point results of new mappings with a contractive iterate at a point in partial metric spaces. Our results generalize and unify some results of Sehgal, Guseman and Ćirić for mappings with a generalized contractive iterate at a point to partial metric spaces. We give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.

Some Fixed Point Results for a Sequence of Mappings on G‐Metric Space

AbstractIn the setting of generalized metric spaces, so called G‐metric spaced introduced by Z. Mustafa and B. Sims in 2006, some fixed point results for mappings with contractive iterate at a point and common fixed point results for infinite family of self mappings will be presented. The results are generalizations of well known results in the metric space. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fixed Point and Subfixed Point for Fuzzy Mappings in Generalized Metric Fuzzy Spaces

A generalized metric in space of set of fuzzy sets is introduced. We prove some common fixed point for contractive iterate at the point and orbitally contractive at the point fuzzy mappings and subfixed point results for family of mappings satisfying generalized contractive conditions in generalized metric fuzzy spaces.

Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces

Abstract Common fixed point results are obtained in 0-complete partial metric spaces under various contractive conditions, including g-quasicontractions and mappings with a contractive iterate. In this way, several results obtained recently are generalized. Examples are provided when these results can be applied and neither corresponding metric results nor the results with the standard completeness assumption of the underlying partial metric space can. MSC:47H10, 54H25.

On Ćirić generalization of mappings with a contractive iterate at a point in G-metric spaces

Main results of this paper are fixed point theorems for mappings with a generalized contractive iterate at a point in G-metric spaces which are generalizations of the well-known results in metric spaces.

A fixed point result for mappings with contractive iterate at a point in G-metric spaces

Using the setting of generalized metric space, so called G-metric space, a fixed point theorems for mappings with a contractive iterate at a point are proved. This result generalize well known comparable result.

On Ćirić maps with a generalized contractive iterate at a point and Fisher’s quasi-contractions in cone metric spaces

In this paper, we generalize and unify some results of Sehgal and Guseman, and Ćirić’s theorem for mappings with a generalized contractive iterate at a point to cone metric spaces, in which the cone does not need to be normal. As corollaries, we obtain recent results of Huang and Zhang, and Raja and Vaezpour. Furthermore, we introduce the definition of Fisher quasi-contractions on cone metric spaces and study their properties. Among other things, using new method of proof, we solve the open problem for the interval of contractive constant λ of (Ćirić) quasi-contraction in non-normal cone metric spaces, and as sn immediate corollary, we recover the recent result of Rezapour and Hamlbarani.

On Mappings with Contractive Iterate at a Point in Generalized Metric Spaces

AbstractUsing the setting of generalized metric space, the so-called G-metric space, fixed point theorems for mappings with a contractive and a generalized contractive iterate at a point are proved. These results generalize some comparable results in the literature. A common fixed point result is also proved.

Analysis of orthogonality and of orbits in affine iterated function systems

We introduce a duality for affine iterated function systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine mappings. We build a duality for such systems by scaling in two directions: fractals in the small by contractive iterations, and fractals in the large by recursion involving iteration of an expansive matrix. By a fractal in the small we mean a compact attractor X supporting Hutchinson’s canonical measure μ, and we ask when μ is a spectral measure, i.e., when the Hilbert space $${L^2( \mu)}$$ has an orthonormal basis (ONB) of exponentials $$\{{e_\lambda, | \lambda \in \Lambda}\}$$ . We further introduce a Fourier duality using a matched pair of such affine systems. Using next certain extreme cycles, and positive powers of the expansive matrix we build fractals in the large which are modeled on lacunary Fourier series and which serve as spectra for X. Our two main results offer simple geometric conditions allowing us to decide when the fractal in the large is a spectrum for X. Our results in turn are illustrated with concrete Sierpinski like fractals in dimensions 2 and 3.

"Approximate Commutative Algebra"

Classical algebra has always considered itself as a discipline in Discrete Mathematics , even when it dealt with objects over the real or complex numbers ( R or C ), where the inherent topology of the number fields would have invited the use of analytic tools. A first change occurred only when the models of applied mathematics required the treatment of larger and larger systems of linear equations and the emerging electronic computers permitted the implementation of algorithms with huge data sets. In the rapidly growing "Numerical Linear Algebra", norms and distances, contractive iterations etc. were used as standard tools: Classical linear algebra over R and C became embedded into Analysis. (As a consequence, in the 2000 Mathematics Subject Classification of the AMS, "Numerical Linear Algebra" is not listed as a subdiscipline of Algebra but of Numerical Analysis.)

On weak convergence of iterates in quantum Lp‐spaces(p ≥ 1)

Equivalent conditions are obtained for weak convergence of iterates of positive contractions in the L1‐spaces for general von Neumann algebra and general JBW algebras, as well as for Segal‐Dixmier Lp‐spaces (1 ≤ p < ∞) affiliated to semifinite von Neumann algebras and semifinite JBW algebras without direct summands of type I2.

Iterative solutions for zeros of accretive operators

AbstractTwo iterative schemes are designed to approach zeros of m–accretive operators in Banach spaces. The first one is a kind of contractive iteration process involving with the resolvent and the second one is an averaged iteration process of the identity and the resolvent. Strong convergence for the first scheme and weak convergence for the second scheme are proved. The second scheme is also shown to have superlinear rate of convergence.

Uniform estimates in two periodic homogenization problems

We analyze two partial differential equations that are posed on perforated domains. We provide a priori estimates that do not depend on the size of the perforation: A sequence of solutions is uniformly bounded in a Sobolev space of regular functions. The first homogenization problem concerns the Laplace and the mean-curvature operator with Neumann boundary conditions. We derive uniform Lipschitz estimates for the solutions. The result is used in the analysis of a free boundary system of fluid mechanics. A contractive iteration yields the existence of solutions and uniform estimates. The key is the use of function spaces that are different from the usual Lp-spaces. © 2000 John Wiley & Sons, Inc.