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1
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Two fixed point theorems for generalized contractions with constants in complete metric space

100%
Popescu O.
Open Mathematics
|
2009
|
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.
2
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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.
3
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Fixed point theorems for cyclic contractive mappings via altering distance functions in metric-like spaces

81%
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.
4
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On the weakly(α, ψ, ξ)-contractive condition for multi-valued operators in metric spaces and related fixed point results

81%
Kutbi M. A., Sintunavarat W.
Open Mathematics
|
2016
|
tom 14
|
nr 1
167-180
EN
The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.
5
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Multivalued fractals in b-metric spaces

81%
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.
6
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A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

81%
Popa V.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
119-129
EN
In this paper, a general fixed point theorem for cyclic multi-valued mappings satisfying an implicit relation from [19] different from implicit relations used in [13] and [23], generalizing some results from [22], [15], [13], [14], [16], [10] and from other papers, is proved.
7
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Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

81%
Sawangsup K., Sintunavarat W.
Open Mathematics
|
2017
|
tom 15
|
nr 1
111-125
EN
The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation. Finally, as numerical experiments, we approximate the definite solution of a nonlinear matrix equation using MATLAB.
8
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A note on “Some results on multi-valued weakly Jungck mappings in b-metric space”

81%
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.
9
Content available remote

Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

81%
Kir M., Yolacan E., Kiziltunc H.
Open Mathematics
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2017
|
tom 15
|
nr 1
734-744
EN
The purpose of this paper is to present some existence results for coupled fixed point of a (φ,ψ) -contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the results.
10
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Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

81%
Kumam P., Sarwar M., Zada M. B.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
89-110
EN
The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.
11
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Solution to Fredholm integral inclusions via ( F, δ b )-contractions

62%
Nashine H. K., Agarwal R. P., Kadelburg Z.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1053-1064
EN
We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.
12
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Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces

62%
Alagoz O., Gunduz B., Akbulut S.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1065-1073
EN
In this article we modify an iteration process to prove strong convergence and Δ- convergence theorems for a finite family of nonexpansive multivalued mappings in hyperbolic spaces. The results presented here extend some existing results in the literature.
13
Content available remote

Invariant sets and Knaster-Tarski principle

62%
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.
14
Content available remote

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

52%
Alsulami H. H., Gülyaz S., Karapınar E., Erhan İ. M.
Open Mathematics
|
2016
|
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.
15
Content available remote

Fixed points for cyclic orbital generalized contractions on complete metric spaces

52%
Karapınar E., Romaguera S., Taş K.
Open Mathematics
|
2013
|
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.
16
Content available remote

Non-self mappings in modular spaces and common fixed point theorems

52%
Razani A., Rakočević V., Goodarzi Z.
Open Mathematics
|
2010
|
tom 8
|
nr 2
357-366
EN
The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.
17
Content available remote

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

52%
Kim K. S.
Open Mathematics
|
2017
|
tom 15
|
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.
18
Content available remote

Fixed point results for multivalued contractions on ordered gauge spaces

52%
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].
19
Content available remote

A cohomological index of Fuller type for parameterized set-valued maps in normed spaces

43%
Skiba R.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1164-1197
EN
We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
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