Related papers: Wardowski implicit contractions in metric spaces
We introduce a novel concept of convergence for Markovian processes within Orlicz spaces, extending beyond the conventional approach associated with $L_p$ spaces. After showing that Markovian operators are contractive in Orlicz spaces, our…
The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike…
In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators…
In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. The obtained results extend,…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
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…
Dimensional types of metric scattered spaces are investigated. Revised proofs of Mazurkiewicz-Sierpi\'nski and Knaster-Urbanik theorems are presented. Embeddable properties of countable metric spaces are generalized onto uncountable metric…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
We look at $d$-point extensions of a rotation of angle $\alpha$ with $r$ marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of \cite{fh2}. We study the…
We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises…
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and…
This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. P\'ales, building on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515-524 (2017)]. By applying…
A description of continuous rigid motion compatible Minkowski valuations is established. As an application, we present a Brunn-Minkowski type inequality for intrinsic volumes of these valuations.
In this note, we obtianed hypercontractive inequalities between different weighted Bergman spaces. In addition, we establish Nikol'ski\u{\i}-type inequalities for weighted Bergman spaces with optimal constants.
Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik \cite{Bartnik_energy}. We show that, for any metric on $\bar{B}_1$ that is close enough to the…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
A new model of fracture mechanics considered previously by Sendova and Walton \cite{SendovaWalton2010}, Zemlyanova \cite{Zemlyanova2013}, and Zemlyanova and Walton \cite{Zemlyanova2012} is further developed on the example of a mixed mode…
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology…
We introduce a large class of mappings, called enriched contractions, which includes, amongst many other contractive type mappings, the Picard-Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a…
Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal.,…