The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions.
In this paper, inspired by the concept of $(ϕ, F)-$contraction in metric spaces, introduced by Wardowski.
We present the notion of $(ϕ, F)-$contraction in $b-$rectangular metric spaces to study the existence and uniqueness of fixed point for the mappings in this spaces. Our results improve many existing results.
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as well and prove some topological and convergence properties under the symmetric convergence. Some examples are given to illustrate the proven results and enrich the new introduced metric type spaces.
In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality as follows: \begin{equation*} d(x, y)\leqα(x, u)d(x, u)+α(u, v)d(u, v)+α(v, y)d(v, y), \end{equation*} for all distinct $x, y, u, v\in X$ with the function $α: X\times X\rightarrow[1,\infty[$. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.
Locally Convex Valued Rectangular Metric Spaces and The Kannan's Fixed Point Theorem
引入了矩形TVS-锥度量空间，并证明了Kannan的不动点定理.两种方法的证明。首先利用空间本身的结构用直接法证明了定理。其次，我们使用了杜伟世最近在[A note on cone metric不动点theory and its equivalents，{Nonlinear Analysis}，72（5），2259 -2261（2010）]中使用的非线性标量化。证明了Banach压缩原理在锥度量空间和一般度量空间中的等价性。证明过程中对局部凸拓扑向量空间的锥不作任何正规性假设，推广了已有的结果。
Fixed point theorems for Meir-Keeler type contractions in metric spaces
我们建立了一个简单而强大的引理，提供了一个标准的序列在度量空间柯西。利用这个引理，很容易地证明了Picard迭代序列$\{T^nx\}$（其中$T$是Meir-Keeler型的压缩序列或渐近压缩序列）是Cauchy序列.作为应用，对满足Meir-Keeler型压缩条件的完全度量空间的连续渐近正则自映射的不动点存在性的几个已知结果给出了新的简单证明.这些结果包括Proinov在[Petko D. Proinov，度量空间中的不动点定理，非线性分析。\textbf{46}（2006）546- 557]中，Suzuki的渐近压缩的不动点定理[Tomonari Suzuki，A definitive result on asymptomatic contractions，J. Math. Anal. \textbf{335}（2007）707- 715]等。我们还证明了一些新的不动点定理。
Arithmetic-geometric mean, additive, and multiplicative contractions: New generalizations of the Banach contraction principle
Manipur University（曼尼普尔大学）；Manipur Institute of Technology（曼尼普尔理工学院）；Institute of Applied Mathematics and Mechanics of the NAS of Ukraine（乌克兰国家科学院应用数学与力学研究所）；Institute of Mathematics of the NAS of Ukraine（乌克兰国家科学院数学研究所）
In the year 2021, Beg et al. \cite{beg} [J. Fixed Point Theory Appl.(2021)] introduced two classes of non-self mappings namely, generalized $F$-proximal contraction of the first kind and generalized $F$-proximal contraction of the second kind. Then authors studied the existence and uniqueness of best proximity points for this two classes of mappings. In this short note, we show that the existence of best proximity point for generalized $F$-proximal contraction of the first kind follows from the same conclusion in fixed point theory.
Startpoints (resp. endpoints) can be defined as "oriented fixed points". They arise naturally in the study of fixed for multi-valued maps defined on quasi-metric spaces. In this article, we give a new result in the startpoint theory for quasi-pseudometric spaces. The result we present is obtained via a generalized weakly contractive set-valued map.
In this paper, we introduce a generalization of rectangular $b-$metric spaces, by changing the rectangular inequality as follows \begin{equation*} ρ(x,y)\le θ(x,y,u,v)[ρ(x,u)+ρ(u,v)+ρ(v,y)], \end{equation*}% for all distinct$\ x,y,u,v\in X.$ We prove some fixed-point theorems and we use our results to present a nice application in last section of this paper. Moreover, in the conclusion we present some new open questions.
Nonlinear contractions in metric spaces under locally T-transitive binary relations
本文在具有局部T-传递二元关系的度量空间中，给出了Boil-Wong不动点定理的一个变形，在泛关系下，它退化为Boil-Wong（Proc.Amer.Math.Soc.20（1969）458-464）和Jotic（Indian J. Pure Appl.Math.26（1995）947-952）的不动点定理.此外，我们的结果扩展了其他几个众所周知的不动点定理，例如：Alam和Imdad（J.不动点理论应用17（4）（2015）693-702）以及Karapinar和Roldan-Lopez-de-Hierro（J. Inequal. 2014：522（2014）12 pp）。
This paper investigates whether some fixed point theorems for quasi-contractions on metric spaces introduced by Cirìc in [1] and generalised by Kumam et al. in [2] can be improved further. It turns out that the answer is negative. We provide two examples of complete metric spaces and two operators without fixed points. We prove that for any possible straightforward relaxation of generalised quasi-contractive conditions, one of these operators satisfies the condition.
Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces
本文证明了S. G. Matthews在1994年关于0-完备部分度量空间的结果可以推广到循环映射.然而，D. Ilić，V. Pavlović and V. Rakoucević in“Some new extensions of Banach's constraction principle to partial度量空间，Appl. Math. Lett. 24（2011），1326--1330”在完备的部分度量空间上不能推广到循环映射。最后通过一些例子说明了所得结果的有效性.此外，我们推广了W. A.柯克，P.S. Srinivasan和P. Veeramani，“满足循环压缩条件的映射的不动点，不动点理论4（1）（2003），79 - 89”.最后，Edelstein型定理也被推广到循环分解中的一个集合是0-紧的情况。
The aim of this study to investigate the existence of solutions for the following nonlocal integral boundary value problem of Caputo type fractional differential inclusions. To achieve our goals, we take advantage of fixed point theorems for multivalued mappings satisfying a new class of contractive conditions in the setting of complete metric spaces. We derive new fixed point results which extend and improve many results in the literature by means of this new class of contractions. We also supply some examples to support the new theory.
In this paper, we introduced two new generalized metric spaces called partial b_{v}(s) and b_{v}(θ) metric spaces which extend b_{v}(s) metric space, b-metric space, rectangular metric space, v-generalized metric space, partial metric space, partial b-metric space, partial rectangular b-metric space and so on. We proved some famous theorems such as Banach, Kannan and Reich fixed point theorems in these spaces. Also, we give definition of partial v-generalized metric space and show that these fixed point theorems are valid in this space. We also give numerical examples to support our definition…
Recently, In the year 2020, Altun et al. \cite{AL} introduced the notion of $p$-proximal contractions and discussed about best proximity point results for this class of mappings. Then in the year 2021, Gabeleh and Markin \cite{GB} showed that the best proximity point theorem proved by Altun et al. in \cite{AL} follows from the fixed point theory. In this short note, we show that if the $p$-proximal contraction constant $k<\frac{1}{3}$ then the existence of best proximity point for $p$-proximal contractions follows from the celebrated Banach contraction principle.
It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some fixed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems …
