The double-controlled metric-type space (X,D) is a metric space in which the triangle inequality has the form D(η,μ)≤ζ1(η,θ)D(η,θ)+ζ2(θ,μ)D(θ,μ) for all η,θ,μ∈X. The maps ζ1,ζ2:X×X→1,∞) are called ...control functions. In this paper, we introduce a novel generalization of a metric space called a double-composed metric space, where the triangle inequality has the form D(η,μ)≤αD(η,θ)+βD(θ,μ) for all η,θ,μ∈X. In our new space, the control functions α,β:0,∞)→0,∞) are composed of the metric D in the triangle inequality, where the control functions ζ1,ζ2:X×X→1,∞) in a double-controlled metric-type space are multiplied with the metric D. We establish some fixed-point theorems along with the examples and applications.
In this paper, the notion of rectangular S-metric spaces which extends rectangular metric spaces introduced by Branciari is introduced. Analogues of the some well known fixed point theorems are ...proved in this space. These results generalize many known results in fixed point theory.
Compact inclusions between variable Hölder spaces Górka, Przemysław; Ruiz, César; Sanchiz, Mauro
Journal of mathematical analysis and applications,
10/2024, Letnik:
538, Številka:
1
Journal Article
Recenzirano
We give a sufficient condition for the inclusion between two variable order Hölder spaces be compact. In some cases, mostly asking log-Hölder continuity in one of the order functions, we find a ...criterion for the inclusion between variable order Hölder spaces to be compact. We consider two variable order functions as well as one variable order functions.
This paper surveys regarding solutions of linear and nonlinear integral equations through fixed point theorem. Banach's contraction mapping principle is the most widely applied fixed point theorem in ...all of analysis with special applications to the theory of integral equations. Over a decade researchers have generalized the definition of a metric space and using the technique of fixed point have found solutions to many linear and nonlinear Volterra-Fredholm integral equations.
The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular ...metric spaces. As applications of our theorems, we deduce certain well-known results in
-metric spaces as corollaries.
In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus ...on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.
Sedghi
et al.
(Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a
S
-metric as a generalized metric in 3-tuples
S
:
X
3
→
0
,
∞
)
, where
X
is a nonempty set. The aim of this paper is to ...introduce the concept of an
n
-tuple metric
A
:
X
n
→
0
,
∞
)
and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered
A
-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.
An iterated function system consists of a complete metric space (X,d) and a finite family of contractions fsub.1 ,⋯,fsub.n :X→X. A generalized iterated function system comprises a finite family of ...contractions defined on the Cartesian product Xsup.m with values in X. In this paper, we want to investigate generalized iterated function systems in the more general setting of b-metric spaces. We prove that such a system admits a unique attractor and, under some further restrictions on the b-metric, it depends continuously on parameters. We also provide two examples of generalized iterated function systems defined on a particular b-metric space and find the corresponding attractors.
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