New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator

Abstract The main object of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of meromorphic multivalent starlike functions, which are defined here by means of a newly defined q-linear differential operator.

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Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Symmetry ◽

10.3390/sym13101840 ◽

2021 ◽

Vol 13 (10) ◽

pp. 1840

Author(s):

Lei Shi ◽

Bakhtiar Ahmad ◽

Nazar Khan ◽

Muhammad Ghaffar Khan ◽

Serkan Araci ◽

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Keyword(s):

Differential Operator ◽

Convex Functions ◽

Starlike Functions ◽

Distortion Theorem ◽

Coefficient Estimates ◽

Radius Of Starlikeness ◽

Growth Theorem ◽

New Class ◽

Radius Of Convexity

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

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A Class of Harmonic Starlike Functions defined by Multiplier Transformation

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.36 ◽

2020 ◽

pp. 455-469

Author(s):

Deepali Khurana ◽

Raj Kumar ◽

Sibel Yalcin

Keyword(s):

Convex Combination ◽

Univalent Functions ◽

Extreme Points ◽

Starlike Functions ◽

Harmonic Mappings ◽

Distortion Bounds ◽

Radius Of Convexity ◽

Univalent Harmonic Mappings ◽

Harmonic Starlike ◽

Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations

Canadian Mathematical Bulletin ◽

10.4153/cmb-1988-012-0 ◽

1988 ◽

Vol 31 (1) ◽

pp. 79-84

Author(s):

P. W. Eloe ◽

P. L. Saintignon

Keyword(s):

Differential Operator ◽

Differential Equations ◽

Boundary Value Problem ◽

Ordinary Differential Equations ◽

Linear Differential Operator ◽

Boundary Value ◽

Linear Differential ◽

Type Boundary ◽

Sign Conditions ◽

Conjugate Type

AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.

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