The main object of this paper is to introduce and investigate a subclass U(λ, α, β, k) of normalized analytic functions in the open unit disk ∆, which generalizes the familiar class of uniformly convex functions. The various properties and characteristics for functions belonging to the class U(λ, α, β, k) derived here include (for example) a characterization theorem, coefficient inequalities an...

Delayed renewal process and delayed renewal reward process are introduced in the framework of uncertainty theory and their uncertainty distributions are provided. Furthermore, delayed renewal theorem on the limit value of the expected renewal rate of the process and delayed renewal reward theorem on the limit value of the long-run expected reward per unit time are presented. At last, some examp...

We study Toeplitz operators on the Hardy spaces of connected compact abelian groups and of tube-type bounded symmetric domains. A representation theorem for these operators and for classes of abstract Toeplitz elements in C*-algebras is proved. This is used to give a unified treatment to index theory in this setting, and a variety of new index theorems are proved that generalize the Gohberg–Kre...

We adapt Sarason’s proof of the Julia-Caratheodory theorem to the class of Schur-Agler mappings of the unit ball, obtaining a strengthened form of this theorem. In particular those quantities which appear in the classical theorem and depend only on the component of the mapping in the complex normal direction have K-limits (not just restricted K-limits) at the boundary. Let B denote the open uni...

In this paper we obtain a multivariable commutator lifting inequality, which extends to several variables a recent result of Foiaş, Frazho, and Kaashoek. The inequality yields a multivariable lifting theorem generalizing the noncommutative commutant lifting theorem. This is used to solve new operator-valued interpolation problems of SchurCarathéodory, Nevanlinna-Pick, and Sarason type on Fock s...

In the present paper, we introduce and investigate an interesting subclass K λ s (h) of analytic and close-to-convex functions in the open unit disk U . For functions belonging to the class K λ s (h) , we derive several properties as the convolution, the coefficient bounds, the covering theorem, the inclusion relationships as well as distortion theorem. The various results presented here would ...

Let $(*) denote the family of subsets of the unit square defined to be of first category (Lebesgue measure zero) in almost every vertical line in the sense of measure (category). Theorem 1. (i) * and ^ are o-ideals. (ii) The union of $ or ty is IX I. (iii) The complement of each member of $ or V contains a set of power c belonging to $ and ty, respectively, (iv) 77ie unit square may be represen...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

If each four spheres in a set of five unit spheres in R have nonempty intersection, then all five spheres have nonempty intersection. This result is proved using Grace’s theorem: the circumsphere of a tetrahedron encloses none of its escribed spheres. This paper provides self-contained proofs of these results; including Schläfli’s double six theorem and modified version of Lie’s line-sphere tra...

We generalize Chirka’s theorem on the extension of functions holomorphic in a neighbourhood of Γ (F )∪ (∂D ×D) – where D is the open unit disc and Γ (F ) is the graph of a continuous D-valued function F – to the bidisc. We extend holomorphic functions by applying the Kontinuitätssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by ...