Related papers: Remarks on Fixed Point Assertions in Digital Topol…
In this oaper, we prove some fixed point theorems in metric vector spaces, in which the continuity is not required for the considered mappings to satisfy. We provide some concrete examples to demonstrate these theorems. We also give some…
Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…
Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a…
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…
Digital topological methods are often used on computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a…
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces…
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
The main aim of this paper is to study of fixed point theory in partial cone metric spaces. Infact, some common fixed point theorems for two mappings in partial cone metric spaces are obtained.
Recently, a new geometric approach which is called the fixed-circle problem has been gained to fixed-point theory. The problem is introduced and studied using different techniques on metric spaces. In this paper, we consider the…
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
We are concerned with the study of fixed points for mappings $T: X\to X$, where $(X,G)$ is a $G$-metric space in the sense of Mustafa and Sims. After the publication of the paper [Journal of Nonlinear and Convex Analysis. 7(2) (2006)…
In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.