Search

In this paper, we derive some bounds for the real parts and arguments of the functionals given by ... where Js;b is the widely-investigated Srivastava-Attiya operator defined on the class of normalized analytic functions f in the open unit disk ... with suitable real parameters s and b. These results reduce upon specialization to some well-known inclusion relationships for several classes of functions with given geometric properties. We also make a comparison between one of the results obtained here and an already known result for some specific cases. [ABSTRACT FROM AUTHOR]

In this paper, we present the best possible parameters α1, α2, α3 and β1, β2, β3 such that the double inequalities Cα1 (a; b)G1-α1 (a, b) < T(a, b) < Cβ1 (a, b)G1-β1 (a, b); α2C(a, b) + (1 - α2)G(a, b) < T(a, b) < β2C(a, b) + (1 - β2)G(a, b), α3/G(a, b)+1 - α3/C(a, b) < 1/T(a, b) < β3/G(a, b) + 1 - β3/C(a, b) hold for all a, b > 0 with a 6 = b, where G(a, b) = √ab, C(a, b) = (a² + b²) / (a+b) and T(a, b) = 2 ∫ π/20 √a2 cos2(t) + b² sin²(t)dt/π are the geometric, contraharmonic and Toader means of a and b, respectively. [ABSTRACT FROM AUTHOR]

The class B¯ B(α) of non-Bazilevič functions was introduced by Obradović. Later, estimates on the second coefficient and Fekete-Szegö functional for normalized analytic functions in the class B¯ B(α) were investigated by Tuneski and Darus. In the present work, sharp estimate on third to eighth coefficients for normalized analytic functions f(z) = z + a2z2 + a3z3 + … ∊ B¯(α) are investigated. Further sharp estimate on the functional ®a2a3 - a4® is also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of analytic functions associated with Mittag-Leffler fuction in the open unit disk. Several properties of functions belonging to this class are derived. [ABSTRACT FROM AUTHOR]

In this paper, we investigate q- analogues of Bieberbach- de Branges theorems and Fekete-Szegö inequalities for certain families of q- convex and q- close-to-convex functions. [ABSTRACT FROM AUTHOR]

The class B¯(α) of non-Bazilevič functions was introduced by Obradović. Later, estimates on the second coefficient and Fekete-Szegö functional for normalized analytic functions in the class B¯(α) were investigated by Tuneski and Darus. In the present work, sharp estimate on third to eighth coefficients for normalized analytic functions f(z) = z + a2z2 + a3z3 + ... ∊ B¯(α) are investigated. Further sharp estimate on the functional ∣a2a3 - a4∣ is also obtained. [ABSTRACT FROM AUTHOR]

This paper discusses Lp approximation error estimates for hybrid interpolation on the unit sphere. This interpolation scheme is integrated by spherical polynomials and radial basis functions. The smooth radial basis functions generated by a strictly positive definite zonal kernel are embedded in a larger native space generated by a less smooth kernel, and the error estimates for hybrid interpolation to a target function from the larger native space are given. In a sense, the results of this paper show that the hybrid interpolation associated with the smooth kernel enjoys the same order of error estimate as hybrid interpolation associated with the less smooth kernel for a target function from the rough native space. [ABSTRACT FROM AUTHOR]

In this paper, in order to solve a class of nonlinear bilevel programming problems, we equivalently transform the nonlinear bilevel programming problems into corresponding single level nonlinear programming problems by using the Karush-Kuhn-Tucker optimality condition. Then, based on penalty function theory, we construct a smooth approximation method for obtaining optimal solutions of classic l1-exact penalty function optimality problems, which is equivalent to the single level nonlinear programming problems. Furthermore, using e-approximate optimal solution theory, we prove convergence of a simple ϵ-approximate optimal algorithm. Finally, through adding parameters in the constraint set of objective function, we prove some perturbation convergence results for solving the nonlinear bilevel programming problems. [ABSTRACT FROM AUTHOR]

The main object of this article is to define a new class of analytic functions using q - Sãlãgean differential operator involving complex order. We obtain coefficient estimates and other useful properties for this new class. [ABSTRACT FROM AUTHOR]

In this paper, we have established the inclusion relations for k-uniformly starlike functions under the (Dqf)(z) operator. We define two new sub-class of k-uniformly starlike functions of order α. Moreover, for functions belonging to these function classes, we investigate necessary and suffcient coeffcient conditions, distortion bounds, extreme points. [ABSTRACT FROM AUTHOR]

Given an analytic standardly normalized function g in D := {z ∊ C : ∣z∣ < 1}, by C(g) will be denoted the class of analytic standardly normalized function f such that Re {eiδzf'(z)/g(z)}>0, z ∊ D, for some δ ∊ (-π/2, π/2). For the class C(g) the Fekete-Szegö problem is examined. [ABSTRACT FROM AUTHOR]

In this paper we consider two types of harmonic mappings w(z) ∊ SH(D, Ω1) and w(z) ∊ SH(픻,R), where 픻 is the unit disk and Ω1, R are the domain defined by (2) and (3). Using the representation of harmonic mappings, we find the sufficient and necessary conditions to make w(z) be a harmonic quasiconformal mapping. Furthermore, we obtain some estimates of w(z). [ABSTRACT FROM AUTHOR]

In this paper, we study the class of harmonic K-quasiconformal mappings of the unit disk U with finite Euclidean areas ∣f(U)∣euc. We first give the Schwarz-pick lemma (cf. [8]) for this class of mappings as follows: ∣fz(z)∣ ≤ √∣f(U)∣euc π(1 - k2) 1 -∣z∣, z ∊ U; where k = K-1/ K+1. Furthermore, we obtain the sharp coefficient estimates of this class of mappings. As an application, for harmonic mappings f ∊ S0H with finite ∣f(U)∣euc we obtain sharp coefficient estimates. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the isometric equivalence problem for the weighted composition operator Wu;φand the composi- tion operator Cφon the Hardy and the Dirichlet space. We show what properties the operators must satisfy to insure that they are isometric equivalent. [ABSTRACT FROM AUTHOR]

In this work we study a new operator IRm,n λ,l defined as the Hadamard product of the multiplier transformation I (m, λ, l) and Ruscheweyh derivative Rn, given by IRm,n λ,l : A → A, IRm,n λ,l f (z) = (I (m, λ, l) * Rn) f (z) and An = {f ϵ H(U) : f (z) = z +an+1zn+1 +..., z ϵ U} is the class of normalized analytic functions with A1 = A. The purpose of this paper is to derive certain subordination and superordination results involving the operator IRm,n λ.l and we establish differential sandwich-type theorems. [ABSTRACT FROM AUTHOR]

We introduce a new subclass of analytic functions in the unit disk U defined by using Cho-Kwon Srivastava integral operator. Inclusion results radius problem and integral preserving properties are investigated. [ABSTRACT FROM AUTHOR]

The object of the present investigation is to solve Fekete-Szegö problem for a new class Vλp (a, c, A,B) of p-valent analytic functions involving the Saitoh operator in the unit disk. We also obtain subordination results and some interesting corollaries for functions in Ap involving this operator. Relevant connections of the results obtained here with those given by earlier workers on the subject are also mentioned. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the essential commutativity and isometry of composition operator and differentiation operator from the Bloch type space to space of all weighted bounded analytic functions in the disk. [ABSTRACT FROM AUTHOR]

In this paper we introduce a kind of complex summation-integral type operators and study the approximation properties of these operators. We obtain a Voronovskaja-type result with quantitative estimate for these operators attached to analytic functions on compact disks. We also study the exact order of approximation. More important, our results show the overconvergence phenomenon for these complex operators. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate some characterization for generalized Bessel functions of first kind to be in the new subclasses G(λ, α) and K(λ, α) of analytic functions. [ABSTRACT FROM AUTHOR]