The results contained in this paper are the result of a study regarding fractional calculus combined with classical theory differential subordination established for analytic complex valued functions. A new operator is introduced by applying Libera integral and order λ Many properties obtained newly defined using famous lemmas proved important scientists concerned geometric function theory, suc...

A new boundary integral operator is introduced for the solution of the sound-soft acoustic scattering problem, i.e. for the exterior problem for Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω...

Let A(p) be the class of functions f : f(z) = z + ∑∞ j=1 ajz p+j analytic in the open unit disc E. Let, for any integer n > −p, fn+p−1(z) = z p (1−z)n+p . We define f (−1) n+p−1(z) by using convolution ? as fn+p−1(z) ? f (−1) n+p−1(z) = z (1−z)n+p . A function p, analytic in E with p(0) = 1, is in the class Pk(ρ) if ∫ 2π 0 ∣∣∣Rep(z)−ρ p−ρ ∣∣∣ dθ ≤ kπ, where z = re, k ≥ 2 and 0 ≤ ρ < p. We use t...

We study operator algebras associated to integral domains. In particular, with respect to a set of natural identities we look at the possible nonselfadjoint operator algebras which encode the ring structure of an integral domain. We show that these algebras give a new class of examples of semicrossed products by discrete semigroups. We investigate the structure of these algebras together with a...

The purpose of this paper is to obtain univalence of a certain nonlinear integral transform of functions belonging to a subclass of analytic functions. We also give several interesting geometric properties of the integral transform.

It is well known that solutions of inhomogeneous differential and integral equations are represented by integral operators. To investigate the stability of solutions, we often use the continuity of corresponding integral operators in the studied function spaces. For instance, the boundedness of Fourier multiplier operators plays a crucial role in the theory of linear PDE’s, especially in the st...

Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar, and (iii) stationary increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time reversibility, the defining properties (i)-(iii) do not, in general, characterize the covariance structure of OFBMs. To circumve...

Let for fixed n ∈ N, Σn denotes the class of function of the following form f(z) = 1 z + ∞ ∑ k=n akz , which are analytic in the punctured open unit disk ∆∗ = {z ∈ C : 0 < |z| < 1}. In the present paper we defined and studied an operator in F (z) = [ c+ 1− μ zc+1 ∫ z 0 ( f(t) t )μ tdt ] 1 μ , for f ∈ Σn and c+ 1− μ > 0.

In this paper, we consider a general integral operator Gn(z). The main object of the present paper is to study some properties of this integral operator on the classes S∗(α), K(α), M(β), N (β) and KD(μ, β).

In the present paper, we introduce a general integral operator and study mapping properties on some subclasses of analytic univalent functions. Relevant connections of the results presented here with various known results are briefly indicated. 2000 Mathematics Subject Classification: 30C45.