• Title/Summary/Keyword: Janowski functions

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A FEW RESULTS ON JANOWSKI FUNCTIONS ASSOCIATED WITH k-SYMMETRIC POINTS

  • Al Sarari, Fuad S;Latha, Sridhar;Darus, Maslina
    • Korean Journal of Mathematics
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    • v.25 no.3
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    • pp.389-403
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    • 2017
  • The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with respect to k-symmetric points. We also study certain interesting properties like covering theorem, convolution condition, neighborhood results and argument theorem.

ON GENERALIZATION OF BI-PSEUDO-STARLIKE FUNCTIONS

  • SHAH, SHUJAAT ALI;NOOR, KHALIDA INAYAT
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.341-350
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    • 2022
  • We introduce certain subclasses of bi-univalent functions related to the strongly Janowski functions and discuss the Taylor-Maclaurin coefficients |a2| and |a3| for the newly defined classes. Also, we deduce certain new results and known results as special cases of our investigation.

CERTAIN SUBCLASS OF STRONGLY MEROMORPHIC CLOSE-TO-CONVEX FUNCTIONS

  • Gagandeep Singh;Gurcharanjit Singh; Navyodh Singh
    • Korean Journal of Mathematics
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    • v.32 no.1
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    • pp.73-82
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    • 2024
  • The purpose of this paper is to introduce a new subclass of strongly meromorphic close-to-convex functions by subordinating to generalized Janowski function. We investigate several properties for this class such as coefficient estimates, inclusion relationship, distortion property, argument property and radius of meromorphic convexity. Various earlier known results follow as particular cases.

A CERTAIN SUBCLASS OF JANOWSKI TYPE FUNCTIONS ASSOCIATED WITH κ-SYMMETRIC POINTS

  • Kwon, Ohsang;Sim, Youngjae
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.143-154
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    • 2013
  • We introduce a subclass $S_s^{({\kappa})}$(A,B) (-1 ${\leq}$ B < A ${\leq}$ 1) of functions which are analytic in the open unit disk and close-to-convex with respect to ${\kappa}$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.

First Order Differential Subordinations for Carathéodory Functions

  • Gandhi, Shweta;Kumar, Sushil;Ravichandran, V.
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.257-270
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    • 2018
  • The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between $Carath{\acute{e}}odory$ functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.

PARTIAL SUMS AND NEIGHBORHOODS OF JANOWSKI-TYPE SUBCLASSES OF MEROMORPHIC FUNCTIONS

  • Abdullah Alatawi;Maslina Darus
    • Korean Journal of Mathematics
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    • v.31 no.3
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    • pp.259-267
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    • 2023
  • The paper presents the introduction of a novel linear derivative operator for meromorphic functions that are linked with q-calculus. Using the linear derivative operator, a new category of meromorphic functions is generated in the paper. We obtain sufficient conditions and show some properties of functions belonging to these subclasses. The partial sums of its sequence and the q-neighborhoods problem are solved.

HIGHER ORDER CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH RUSCHEWEYH DERIVATIVE OPERATOR

  • NOOR, KHALIDA INAYAT;SHAH, SHUJAAT ALI
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.133-143
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    • 2021
  • The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.

ON SOME DIFFERENTIAL SUBORDINATION INVOLVING THE BESSEL-STRUVE KERNEL FUNCTION

  • Al-Dhuain, Mohammed;Mondal, Saiful R.
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.445-458
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    • 2018
  • In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. Some open problems with this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.

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.