On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

Abstract

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zu p (z) to be in the classes SP p (α, β) and UCSP(α, β) of uniformly spirallike functions and also give necessary and sufficient conditions for z(2 − u p (z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ, c)f to be in UCSPT (α, β) provided that the function f is in the class R τ (A, B). Finally, we give conditions for the integral operator G(κ, c, z) = z 0 (2 − u p (t))dt to be in the class UCSPT (α, β). Several corollaries and consequences of the main results are also considered.Mathematics Subject Classification (2010): 30C45.

Subclasses of analytic functions associated with Pascal distribution series

“…Motivated by several earlier results on connections between various subclasses of analytic and univalent functions, by using hypergeometric functions (see for example, [2,7,10,19,20]) and by using various distributions such as Yule-Simon distribution, Logarithmic distribution, Poisson distribution, Binomial distribution, Beta-Binomial distribution, Zeta distribution, Geometric distribution and Bernoulli distribution (see for example, [4,6,8,9,12,13,18,15]), in this paper, we determine the necessary and sufficient conditions for Φ m q (z) to be in our classes S(k, λ) and C(k, λ) and connections of these subclasses with R τ (A, B). Finally, we give conditions for the integral operator…”

Classes of Harmonic Functions Related to Mittag-Leffler Function

“…∪ {0}. Inclusion relations between different subclasses of analytic and univalent functions by using hypergeometric functions [10,31], generalized Bessel function [32][33][34] and by the recent investigations related with distribution series [35][36][37][38][39][40][41], were studied in the literature. Very recently, several authors have investigated mapping properties and inclusion results for the families of harmonic univalent functions, including various linear and nonlinear operators (see [42][43][44][45][46][47][48]).…”

An application of Mittag–Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains

“…where * denote the convolution or Hadamard product of two series. Motivated by several earlier results on connections between various subclasses of analytic and univalent functions, using hypergeometric functions (see for example, [31,32,33,34]), generalized Bessel functions (see for example, [35,36]), Struve functions (see for example, [37,38,39]), Poisson distribution series (see for example, [1,40,41,42,43,44]) and Pascal distribution series (see for example, [45,46,47,48,49,50,51]), in this paper we determine conditions for Φ , to be in the classes -…”