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The curvature KT (w) of a contraction T in the Cowen-Douglas class B1(D) is bounded above by the curvature KS∗(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this note, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions o...

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results. Keywords—eak almost Dunford-Pettis operator, almost DunfordPettis o...

The purpose of the present paper is to study a new subclass of harmonic univalent functions associated with fractional calculus operator. We obtain coefficient conditions, distortion bounds and extreme points for this class and discuss a class preserving integral operator. We also show that the class studied in this paper is closed under convolution and convex combination. The results obtained ...

where Dn denotes the differential operator with Dnf(z) = D(Dn−1f(z)) = z[Dn−1f(z)]′ and D◦f(z)= f(z). Remark 1.2. The differential operator Dn was introduced by Sălăgean [5]. For n = 1, B1(α) denotes the class of Bazilević functions with logarithmic growth studied [4, 6, 7], amongst others. In [2], the author established some properties of the class Bn(α) including showing that Bn(α) forms a su...

We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm, and therefore a logarithmic-space isomorphism tes...

The powerset operator, P, is an operator which (1) sends sets to sets,(2) is defined by a positive formula and (3) raises the cardinality of its argument, i.e., |P(x)| > |x|. As a consequence of (3), P has a proper class as least fixed point (the universe itself). In this paper we address the questions: (a) How does P contribute to the generation of the class of all positive operators? (b) Are ...

In the present work, authors introduce a new linear differential operator associated with $ q $-calculus which uses $-derivative operator. For class involving operator, interesting properties like coefficient inequality, growth, distortion, convolution and radii of starlikeness are established. Various connections that earlier works pointed out.