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A generalization of the triangle inequality is introduced by a mapping similar to a t-conorm mapping. This generalization leads us to a notion for which we use the $\star$-metric terminology. We are interested in the topological space…
In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary metric space and generally, a $\Lambda$-metric space, is a topological space, and in…
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.
In a recent article, Khojasteh et al. introduced a new class of simulation functions, Z-contractions, with blending over known contractive conditions in the literature. Subsequently, in this paper, we extend and generalize the results on…
We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.
In the paper we apply some of the results from the theory of ball spaces in the semimetric spaces. This allowed us to obtain some fixed point theorems which we believe to be unknown to this day. We also show the limitations of the ball…
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…
This paper gives a short introduction into the metric theory of spaces with dilations.
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
This study focuses on defining normal and strictly convex structures within Menger cone PM-space. It also presents a shared fixed point theorem for the existence of two self-mappings constructed on a strictly convex probabilistic cone…
We develop a geometric framework that unifies several different combinatorial fixed-point theorems related to Tucker's lemma and Sperner's lemma, showing them to be different geometric manifestations of the same topological phenomena. In…
The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.
In this paper we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler's contraction principle for set-valued functions (see Multi-valued contraction…
In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an $E$-distance. We also give two sufficient conditions under which the fixed point is unique. Our main…
Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…
The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Kannan type mappings on complete cone metric spaces depended on another function.
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
We introduce the concept of $\it{ startpoint}$ and $\it{endpoint}$ for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued…
We introduce a new type of mappings in metric spaces which are three-point analogue of the well-known Kannan type mappings and call them generalized Kannan type mappings. It is shown that in general case such mappings are discontinuous but…
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that…