• Title/Summary/Keyword: Starlike functions

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GEOMETRIC PROPERTIES ON (j, k)-SYMMETRIC FUNCTIONS RELATED TO STARLIKE AND CONVEX FUNCTION

  • Gochhayat, Priyabrat;Prajapati, Anuja
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.455-472
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    • 2022
  • For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST[j,k](A, B) and K[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a23 - a5|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K[j,k](α) for all 0 ≤ α < 1.

Multivalent Harmonic Uniformly Starlike Functions

  • Ahuja, Om;Joshi, Santosh;Sangle, Naveneet
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.545-555
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    • 2009
  • In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

STUDY ON UNIFORMLY CONVEX AND UNIFORMLY STARLIKE MULTIVALENT FUNCTIONS ASSOCIATED WITH LIBERA INTEGRAL OPERATOR

  • Mayyadah Gh. Ahmed;Shamani Supramaniam
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.1
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    • pp.81-93
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    • 2023
  • By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ Ap using this operator.

SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY LOMMEL OPERATOR

  • Altinkaya, Sahsene;Badar, Rizwan Salim;Noor, Khalida Inayat
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.567-574
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    • 2022
  • We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

ON A CLASS OF MEROMORPHICALLY P-VALENT STARLIKE FUNCTIONS

  • Xu NENG;YANG DINGGONG
    • The Pure and Applied Mathematics
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    • v.12 no.1
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    • pp.57-63
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    • 2005
  • Let ∑(p)(p ∈ N) be the class of functions f(z) = z/sup -p/ + α/sub 1-p/ z/sup 1-p/ + α/sub 2-p/z/sup 2-p/ + ... analytic in 0 < |z| < 1 and let M(p, λ, μ)(0 < λ≤ 2 and 2λ(λ - 1) ≤ μ ≤ λ²) denote the class of functions f(z) ∈ ∑(p) which satisfy (equation omitted). The object of the present paper is to derive some properties of functions in the class M(p, λ, μ).

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SUBCLASSES OF k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR

  • Seker, Bilal;Acu, Mugur;Eker, Sevtap Sumer
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.169-182
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    • 2011
  • The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

APPLICATIONS OF DIFFERENTIAL SUBORDINATIONS TO CERTAIN CLASSES OF STARLIKE FUNCTIONS

  • Banga, Shagun;Kumar, S. Sivaprasad
    • Journal of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.331-357
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    • 2020
  • Let p be an analytic function defined on the open unit disk 𝔻. We obtain certain differential subordination implications such as ψ(p) := pλ(z)(α+βp(z)+γ/p(z)+δzp'(z)/pj(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to 𝒫, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy |log(zf'(z)/f(z))| < 1, |(zf'(z)/f(z))2 - 1| < 1 and zf'(z)/f(z) lying in the parabolic region v2 < 2u - 1.