相关论文: An Extension of a Normality Result by Carath\'eodo…
This article aims at finding sufficient conditions for a family of meromorphic functions to be normal by involving partial sharing of sets with differential polynomials. Moreover, corresponding results for normal meromorphic functions are…
We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath\'eodory--Fej\'er--Tur\'an problem. The first variation imposes the additional requirement that the function is…
In this paper, we prove some value distribution results which lead to some normality criteria for a family of analytic functions. These results improve some recent results.
In this paper a quaternionic sharp version of the Carath\'{e}odory theorem is established for slice regular functions with positive real part, which strengthes a weaken version recently established by D. Alpay et. al. using the Herglotz…
We give several new characterizations of Caratheodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
In this article, we extend the foundations of the theory of differential inclusions in the space of compactly supported probability measures, introduced recently by the authors, to the setting of general Wasserstein spaces. In this context,…
We prove representation theorems for Carath\'eodory functions in the setting of Banach spaces.
In this article we prove some normality criteria for a family of meromorphic functions which involves sharing of a non-zero value by certain differential monomials generated by the members of the family. These results generalizes some of…
This paper is concerned with the problem of existence of periodic solutions for perturbative Carath\'{e}odory differential equations. The main result provides sufficient conditions on the averaged equation that guarantee the existence of…
This survey mainly deals with the tilted Carath{\'e}odory class by angle $\lambda$ (denoted by $\mathcal{P}_{\lambda}$) an element of which maps the unit disc into the tilted right half-plane $\{w: \Re e^{i\lambda} w>0\}$. Firstly we will…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.
We prove some extensions of Andrews inequality.
We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carath\'eodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions.…
In this exploratory note we ask the question of what a measure of performance for all tasks is like if we use a weighting of tasks based on a difficulty function. This difficulty function depends on the complexity of the (acceptable)…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
Recently, extensions of gamma and beta functions have been studied by many researchers due to their nice properties and variety of applications in different fields of science. The aim of this note is to investigate generalized inequalities…
We study the Carath\'eodory metric on some generalized Teichm\"uller spaces. Earle showed that the Carath\'eodory metric is complete on any Teichm\"uller space. Miyachi extended this result for Asymptotic Teichm\"uller spaces. We study the…
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.