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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.
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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.
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3
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The minimal displacement problem in the space l ∞

Open Mathematics
|
2012
|
tom 10
|
nr 6
2211-2214
EN
We give a lower bound for the minimal displacement characteristic in the space l ∞.
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.
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5
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Multivalued fractals in b-metric spaces

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.
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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].
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7
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.
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.
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9
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.
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.
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11
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On the existence of ɛ-fixed points

Open Mathematics
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2014
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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.
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12
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Some results on multi-valued weakly jungck mappings in b-metric space

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

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.
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Open Mathematics
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2012
|
tom 10
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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
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
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A fixed point theorem for affine mappings and its application to elasticity theory

Open Mathematics
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2010
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tom 8
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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

Open Mathematics
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2013
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tom 11
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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.
Open Mathematics
|
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.
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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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