The aim of the present paper is to study a certain subclass of harmonic univalent functions with varying arguments defined by Salegean operator. For this class we determine a sufficient coefficient condition, representation theorem, distortion theorem, extreme points. Mathematics Subject Classification: Primary 30C45; Secondary 30C80

and Applied Analysis 3 2. Preliminaries A continuous function f u iv is a complex-valued harmonic function in a domain D ⊂ if both u and v are real harmonic in D. In any simply connected domain, we can write

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Let φ (z) be a fixed analytic and univalent function of the form φ(z) = z + ∑∞ k=2 ckz k and Hφ (ck, δ) be the subclass consisting of analytic and univalent functions f of the form f(z) = z + ∑∞ k=2 akz k which satisfy the inequality ∑∞ k=2 ck |ak| ≤ δ. In this paper, we determine the sharp lower bounds for Re { Dpf(z) Dfn(z) } and Re { Dfn(z) Dpf(z) } , where fn(z) = z + ∑n k=2 akz k be the se...

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in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

We consider finite sequences s ∈ D n where D is a commutative, unital, integral domain. We prove three sets of identities (possibly with repetitions), each involving 2n polynomials associated to s. The right-hand side of these identities is a recursively-defined (non-zero) 'product-of-discrepancies'. There are implied iterative algorithms (of quadratic complexity) for the left-hand side coeffic...