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1
Content available remote

An observation on Kannan mappings

100%
Nakanishi M., Suzuki T.
Open Mathematics
|
2010
|
tom 8
|
nr 1
170-178
EN
In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.
2
Content available remote

An Ulam stability result on quasi-b-metric-like spaces

80%
Alsulami H. H., Gülyaz S., Karapınar E., Erhan İ. M.
Open Mathematics
|
2016
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tom 14
|
nr 1
1087-1103
EN
In this paper a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces are defined. Existence and uniqueness of fixed points for this class of mappings is discussed and the results are applied to Ulam stability problems. Various consequences of the main results are obtained and illustrative examples are presented.
3
Content available remote

Fixed points for cyclic orbital generalized contractions on complete metric spaces

80%
Karapınar E., Romaguera S., Taş K.
Open Mathematics
|
2013
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tom 11
|
nr 3
552-560
EN
We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.
4
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Two fixed point theorems for generalized contractions with constants in complete metric space

80%
Popescu O.
Open Mathematics
|
2009
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tom 7
|
nr 3
529-538
EN
In this paper we prove two fixed point theorems for generalized contractions with constants in complete metric space, which are generalizations of very recent results of Kikkawa and Suzuki.
5
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Fixed point results for multivalued contractions on ordered gauge spaces

80%
Petruşel G.
Open Mathematics
|
2009
|
tom 7
|
nr 3
520-528
EN
The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].
6
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On the Existence and Local Asymptotic Stability of Solutions of Fractional Order Integral Equations

71%
Abbas S. d., Benchohra M.
Commentationes Mathematicae
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2012
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tom 52
|
nr 1
EN
In this paper, we present some results concerning the existence and the local asymptotic stability of solutions for a functional integral equation of fractional order, by using some fixed point theorems.
7
Content available remote

Nonlinear Markov processes in big networks

71%
Li Q.-L.
Special Matrices
|
2016
|
tom 4
|
nr 1
202-217
EN
Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly, a nonlinear Markov process is derived from a large number of big networks with weak interactions, where each big network is described as a continuous-time block-structured Markov process. Secondly, some effective algorithms are given for computing the fixed points of the nonlinear Markov process by means of the UL-type RG-factorization. Finally, the Birkhoff center, the locally stable fixed points, the Lyapunov functions and the relative entropy are developed to analyze stability or metastability of the system of weakly interacting big networks, and several interesting open problems are proposed with detailed interpretation. We believe that the methodology and results given in this paper can be useful and effective in the study of big networks.
8
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Fixed point theorems for cyclic contractive mappings via altering distance functions in metric-like spaces

71%
Chen J., Huang X., Li S.
Open Mathematics
|
2016
|
tom 14
|
nr 1
857-874
EN
In this paper, we introduce two different contractive conditions and prove some new fixed point theorems for cyclic (ψ,ϕ,φ)α-contractive mappings and α-(κ,φ)g-contractive mappings in complete metric-like spaces via altering distance functions. Our results generalize and extend some existing results. Moreover, some examples are given to support the obtained results.
9
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Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

71%
Abdulghafor R., Shahidi F., Zeki A., Turaev S.
Open Mathematics
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2016
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tom 14
|
nr 1
509-519
EN
The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.
10
Content available remote

Convergence and stability of generalizedφ-weak contraction mapping inCAT(0) spaces

71%
Kim K. S.
Open Mathematics
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2017
|
tom 15
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nr 1
1063-1074
EN
The aim of this paper is to prove some fixed point results for generalized φ-weak contraction mapping and study a new concept of stability which is called comparably almost T-stable by using iterative schemes in CAT(0) spaces.
11
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Cone 2-metric space nad Fixed point theorem of contractive mappings

71%
Singh B., Jain S., Bhagat P.
Commentationes Mathematicae
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2012
|
tom 52
|
nr 2
EN
In this paper we introduce cone 2-metric space and prove some fixed point theorems of a contractive mapping on a cone 2-metric space.
12
Content available remote

Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

61%
Yao Y., Cho Y., Liou Y.-C.
Open Mathematics
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2011
|
tom 9
|
nr 3
640-656
EN
In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.
13
Content available remote

Fixed points and iterations of mean-type mappings

61%
Matkowski J.
Open Mathematics
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2012
|
tom 10
|
nr 6
2215-2228
EN
Let (X, d) be a metric space and T: X → X a continuous map. If the sequence (T n)n∈ℕ of iterates of T is pointwise convergent in X, then for any x ∈ X, the limit $$\mu _T (x) = \mathop {\lim }\limits_{n \to \infty } T^n (x)$$ is a fixed point of T. The problem of determining the form of µT leads to the invariance equation µT ○ T = µT, which is difficult to solve in general if the set of fixed points of T is not a singleton. We consider this problem assuming that X = I p, where I is a real interval, p ≥ 2 a fixed positive integer and T is the mean-type mapping M =(M 1,...,M p) of I p. In this paper we give the explicit forms of µM for some classes of mean-type mappings. In particular, the classical Pythagorean harmony proportion can be interpreted as an important invariance equality. Some applications are presented. We show that, in general, the mean-type mappings are not non-expansive.
14
Content available remote

Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

61%
Aqlan M. H., Alsaedi A., Ahmad B., Nieto J. J.
Open Mathematics
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2016
|
tom 14
|
nr 1
723-735
EN
We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
15
Content available remote

An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

61%
Petruşel A., Yao J.-C.
Open Mathematics
|
2009
|
tom 7
|
nr 2
335-347
EN
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.
16
Content available remote

Invariant sets and Knaster-Tarski principle

61%
Leśniak K.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2077-2087
EN
Our aim is to point out the applicability of the Knaster-Tarski fixed point principle to the problem of existence of invariant sets in discrete-time (multivalued) semi-dynamical systems, especially iterated function systems.
17
Content available remote

Multivalued fractals in b-metric spaces

61%
Boriceanu M., Bota M., Petruşel A.
Open Mathematics
|
2010
|
tom 8
|
nr 2
367-377
EN
Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.
18
Content available remote

A note on “Some results on multi-valued weakly Jungck mappings in b-metric space”

61%
Bota M.-F., Karapınar E.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1711-1712
EN
The proofs of Theorems 2.1, 2.2 and 2.3 from [Olatinwo M.O., Some results on multi-valued weakly jungck mappings in b-metric space, Cent. Eur. J. Math., 2008, 6(4), 610–621] base on faulty evaluations. We give here correct but weaker versions of these theorems.
19
Content available remote

On the existence of ɛ-fixed points

61%
Cardinali T.
Open Mathematics
|
2014
|
tom 12
|
nr 9
1320-1329
EN
In this paper we prove some approximate fixed point theorems which extend, in a broad sense, analogous results obtained by Brânzei, Morgan, Scalzo and Tijs in 2003. By assuming also the weak demiclosedness property we state two fixed point theorems. Moreover, we study the existence of ɛ-Nash equilibria.
20
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On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

51%
Kozlowski W. M.
Commentationes Mathematicae
|
2011
|
tom 51
|
nr 1
EN
Let \(C\) be a \(\rho\)-bounded, \(\rho\)-closed, convex subset of a modular function space \(L_\rho\). We investigate the existence of common fixed points for semigroups of nonlinear mappings \(T_t\colon C\to C\), i.e. a family such that \(T_0(x) = x\), \(T_{s+t} = T_s (T_t (x))\), where each \(T_t\) is either \(\rho\)-contraction or \(\rho\)-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
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