Certain results on q-starlike and q-convex error functions

Abstract

The error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. There has been no work in this area for the past four decades. In this article, we estimate the coefficient bounds with q-difference operator for certain classes of the spirallike starlike and convex error function associated with convolution product using subordination as well as quasi-subordination. Though this concept is an untrodden path in the field of complex function theory, it will prove to be an encouraging future study for researchers on error function.

Toeplitz Determinant For Error Starlike & Error Convex Function

“…In the year 2016, Ramachandran et al [13] introduced and defined the following function will be of the form…”

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Normalised Error function has been coined and analyzed in 2018 [13].The concept of normalised error function discussed in [13], motivated us to find the new results of Toeplitz determinant for the subclasses of analytic univalent functions concurrent with error function. By seeing the history of error function in Geometric functions theory, Ramachandran et.

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“…By seeing the history of error function in Geometric functions theory, Ramachandran et. al [13] derived the coefficient estimates followed by the Fekete-Szegö problem for the normalised subclasses of starlike and convex functions associated with error function. Finding coefficient estimates is one of the most provoking concepts in geometric function theory.…”

Properties of λ-Pseudo-Starlike Functions of Complex Order Defined by Subordination

“…Replacing the values of L 1 , L 2 and L 3 of Theorem 4 with the corresponding coefficients of the power series (26), we obtain the next result: Theorem 7. If the function f given by (1) and g given by (9) are inverse functions and if f ∈ P S t λ (α, β; γ; J ; h; A, B), with J defined as in (25), then for the coefficients of g = f −1 , we have:…”

“…Corollary 4 ([12] (Theorem 4)). If the function f given by (1) and g given by (9) are inverse functions and if f ∈ P S 0 1 (0, 0; 1; J ; A, B), with J defined as in (25), then for the coefficients of g = f −1 , we have:…”