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1
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Existence of a common solution for a system of nonlinear integral equations via fixed point methods inb-metric spaces

100%
Yamaod O., Sintunavarat W., Je Cho Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
128-145
EN
In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) =  ∫ a b K 1  (t,r,x(r)) dr, x (t) =  ∫ a b K 2  (t,r,x(r)) dr,       $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$ where a, b ∈ ℝ with a < b, x ∈ C[a, b] (the set of continuous real functions defined on [a, b] ⊆ ℝ) and K1, K2 : [a, b] × [a, b] × ℝ → ℝ are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.
2
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Fixed point theorems for cyclic contractive mappings via altering distance functions in metric-like spaces

100%
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.
3
Content available remote

The minimal displacement problem in the space l ∞

100%
Bolibok K.
Open Mathematics
|
2012
|
tom 10
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nr 6
2211-2214
EN
We give a lower bound for the minimal displacement characteristic in the space l ∞.
4
Content available remote

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

100%
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

100%
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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Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space

100%
Olatinwo M.
Open Mathematics
|
2008
|
tom 6
|
nr 2
335-341
EN
In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts of an A-distance and an E-distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type. Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].
7
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A General Fixed Point Theorem For Implicit Cyclic Multi-Valued Contraction Mappings

100%
Popa V.
Annales Mathematicae Silesianae
|
2015
|
tom 29
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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.
8
Content available remote

Fixed point and multidimensional fixed point theorems with applications to nonlinear matrix equations in terms of weak altering distance functions

100%
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.
9
Content available remote

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

100%
Bota M.-F., Karapınar E.
Open Mathematics
|
2013
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tom 11
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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.
10
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Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

100%
Kir M., Yolacan E., Kiziltunc H.
Open Mathematics
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2017
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tom 15
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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.
11
Content available remote

On the existence of ɛ-fixed points

100%
Cardinali T.
Open Mathematics
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2014
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tom 12
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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.
12
Content available remote

Some results on multi-valued weakly jungck mappings in b-metric space

100%
Olatinwo M.
Open Mathematics
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2008
|
tom 6
|
nr 4
610-621
EN
In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].
13
Content available remote

Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

100%
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.
14
Content available remote

Solution to Fredholm integral inclusions via ( F, δ b )-contractions

76%
Nashine H. K., Agarwal R. P., Kadelburg Z.
Open Mathematics
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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.
15
Content available remote

A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

76%
Przeradzki B.
Open Mathematics
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2012
|
tom 10
|
nr 6
2012-2018
EN
The existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.
16
Content available remote

Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces

76%
Alagoz O., Gunduz B., Akbulut S.
Open Mathematics
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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.
17
Content available remote

A fixed point theorem for affine mappings and its application to elasticity theory

76%
Zubelevich O.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1104-1108
EN
In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
18
Content available remote

Ulam stability for a delay differential equation

76%
Otrocol D., Ilea V.
Open Mathematics
|
2013
|
tom 11
|
nr 7
1296-1303
EN
We study the Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for a delay differential equation. Some examples are given.
19
Content available remote

Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

76%
Amar A.
Open Mathematics
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2013
|
tom 11
|
nr 1
85-93
EN
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
20
Content available remote

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

65%
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.
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