Results 11 to 20 of about 46 (43)
International Journal of Mathematics and Mathematical Sciences, Volume 2014, Issue 1, 2014., 2014 By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions.
K. AL-Shaqsi, Heinrich Begehr
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Definition and Properties of the Libera Operator on Mixed Norm Spaces
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 We consider the action of the operator ℒg(z)=(1-z) -1∫z1 f(ζ) dζ on a class of “mixed norm” spaces of analytic functions on the unit disk, X=Hα,νp,q, defined by the requirement g ∈ X⇔r ↦ (1 − r) αMp(r, g(ν)) ∈ Lq([0,1], dr/(1 − r)), where 1 ≤ p ≤ ∞, 0 < q ≤ ∞, α > 0, and ν is a nonnegative integer.
Miroslav Pavlovic, H. Jafari, Y. Wang
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International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 We introduce a new class of analytic functions by using Komatu integral operator and obtain some subordination results.
Serap Bulut +4 more
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Multipliers on Generalized Mixed Norm Sequence Spaces
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Given 1 ≤ p, q ≤ ∞ and sequences of integers (nk) k and (nk′)k such that nk≤nk′≤nk+1, the generalized mixed norm space ℓℐ(p, q) is defined as those sequences (aj) j such that ((∑j∈Ik |aj|p) 1/p) k∈ℓq where Ik={j∈ℕ0 s.t. nk≤j
Oscar Blasco +2 more
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Generalized k‐Uniformly Close‐to‐Convex Functions Associated with Conic Regions
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close‐to‐convexity.
Khalida Inayat Noor, Muhammad Aslam Noor
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Coefficient Bounds for Certain Subclasses of Analytic Functions Defined by Komatu Integral Operator
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We determine the coeffcient bounds for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non‐homogeneous Cauchy–Euler type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.
Serap Bulut, Yuri Latushkin
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Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 We obtain some subordination‐ and superordination‐preserving properties for a class of multiplier transformations associated with Noor integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich‐type theorems for these transformations are also considered.
Nak Eun Cho +2 more
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Inner Functions in Lipschitz, Besov, and Sobolev Spaces
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We study the membership of inner functions in Besov, Lipschitz, and Hardy‐Sobolev spaces, finding conditions that enable an inner function to be in one of these spaces. Several results in this direction are given that complement or extend previous works on the subject from different authors.
Daniel Girela +3 more
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Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz‐Lerch Zeta Function
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 Let fn(z)=z+∑k=2nakzk be the sequence of partial sums of the analytic function f(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds for ℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)}, and ℜ{fn′(z)/f′(z)}. The usefulness of the main result not only provides the unification of the results discussed in the literature but also generates certain ...
G. Murugusundaramoorthy +3 more
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On an Integral‐Type Operator from Zygmund‐Type Spaces to Mixed‐Norm Spaces on the Unit Ball
Abstract and Applied Analysis, Volume 2010, Issue 1, 2010., 2010 The boundedness and compactness of an integral‐type operator recently introduced by the author from Zygmund‐type spaces to the mixed‐norm space on the unit ball are characterized here.
Stevo Stević, H. B. Thompson
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