Coefficient Inequalities of Functions Associated with Petal Type Domains

Abstract

In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work.

On q‐Convex Functions Defined by the q‐Ruscheweyh Derivative Operator in Conic Regions

“…For more details about the above classes and conic domain, we refer the readers to [20,[25][26][27][28]. Using the q-Ruscheweyh differential operator, we now define the following more general class β − UCV λ q [A, B] of functions associated with the conic domain defined by Janowski functions.…”

“…Using the already proven results of Silverman [16] and Silvia [17] on partial sums of holomorphic functions, we will find the fraction of (1) to its sequence of partial sums y k (z) � z + 􏽐 k n�2 b n z n when the function y(z) has coefficients small enough to satisfy condition (28). We will investigate sharp lower bounds for R y(z)/y k (z)…”

Hankel Determinants and Coefficient Estimates for Starlike Functions Related to Symmetric Booth Lemniscate

“…The class S * cos := S * (cos(ζ)) was introduced by Bano and Raza [9]. For some recent work in this direction, we refer to [10][11][12][13][14][15][16][17][18] and references therein, which include the study of analytic functions associated with certain functions and domains such as sigmoid function, Pascal snail function, cardioid domain, petal-type domain, limacon domain, and nephroid domain. Furthermore, factional and q-fractional derivatives are applied to the classes defined by using the above domains to study various generalizations of the classes of univalent functions.…”

Coefficient Bounds of Kamali-Type Starlike Functions Related with a Limacon-Shaped Domain

“…Gandhi in [33] considered a class S * ðψÞ with ψ = βe ξ + ð1 − βÞð1 + ξÞ, 0 ≤ β ≤ 1, a convex combination of two starlike functions. Further, coefficient inequalities of functions linked with petal type domains were widely discussed by Malik et al ( [34], see also references cited therein). The region bounded by the cardioid specified by the equation…”