Related papers: Fixed points of the Ruelle-Thurston operator and t…

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains…

Elementary transformations of equations $A\psi=\lambda\psi$ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator $A$ are…

We discuss the relation between the existence of fixed points of the Ruelle operator acting on different Banach spaces, with Sullivan's conjecture in holomorphic dynamics.

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…

The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the…

We present a constructive proof of Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions based on the existence of approximate fixed points. And we will show that Brouwer's fixed point…

For a given Beurling-Carleson subset $E$ of the unit circle $\mathbb{T}$ which has positive Lebesgue measure, we give explicit formulas for measurable functions supported on $E$ such that their Cauchy transforms have smooth extensions from…

In this paper, influenced by the ideas from A. Mihail, The canonical projection between the shift space of an IIFS and its attractor as a fixed point, Fixed Point Theory Appl., 2015, Paper No. 75, 15 p., we associate to every generalized…

In this work, we establish some coincidence point results for self-mappings satisfying rational type contractions in generalized metric spaces in the sense of Branciari [7]. Presented coincidence point theorems weak and extend numerous…

We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type…

In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Frechet spaces and also operators having properties weaker…

In this paper we consider partial metric spaces in the sense of O'Neill. We introduce the notions of strong partial metric spaces and Cauchy functions. We prove a fixed point theorem for such spaces and functions that improves Matthews'…

In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…

We introduce the notion of Dunkl positive definite and strictly positive definite functions on $\mathbb{R}^{d}$. This done by the use of the properties of Dunkl translation. We establish the analogue of Bochner's theorem in Dunkl setting.…

The \emph{Continuity Problem} is the question whether effective operators are continuous, where an effective operator $F$ is a function on a space of constructively given objects $x$, defined by mapping construction instructions for $x$ to…

For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…

We consider Toeplitz operators in the Fock space, under rather general conditions imposed on the symbols. It is proved that if the operator has finite rank and the symbol is a function then the operator and the symbol should be zero. The…

In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…

In the seventies', Zehnder found a Nash-Moser type implicit function theorem in the analytic set-up. This theorem has found many applications in dynamical systems although its applications require, as a general rule, some efforts. We…