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This study defines three novel classes of bi‐univalent functions connected to generalized telephone numbers for the first time. We produced assessments about the Taylor–Maclaurin coefficients |a2| and |a3| and Fekete–Szegö functional problems for functions involving these novel subclasses for functions in every one regarding these three bi‐univalent function classes. Additional findings are anticipated to emerge after expertise the factors included in our significant outcomes, which have not yet been investigated by subordinating with generalized telephone numbers. [ABSTRACT FROM AUTHOR]

The focus of the present work is on the establishment and investigation of the coefficient estimates of two new subclasses of bi-close-to-convex functions and bi-concave functions; these are of an Ozaki type and involve a modified Caputo's fractional operator that is associated with three-leaf functions in the open unit disc. The classes are defined using the notion of subordination based on the previously established fractional integral operators and classes of starlike functions associated with a three-leaf function. For functions in these classes, the Fekete-Szegö inequalities and the initial coefficients, | a 2 | and | a 3 | , are discussed. Several new implications of the findings are also highlighted as corollaries. [ABSTRACT FROM AUTHOR]

In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects such as coefficient bounds, convolution conservation, and convexity constraints. Next, using sufficiency criteria, we calculate the sharp bounds of the real parts of the ratios of harmonic functions to their sequences of partial sums. In addition, for the first time some of the interesting implications of the q-Srivastava–Attiya operator in harmonic functions are also included. [ABSTRACT FROM AUTHOR]

In this article we introduce three new subclasses of the class of bi-univalent functions Σ , namely HG Σ , GM Σ (μ) and G Σ (λ) , by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates a 2 and a 3 of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions. [ABSTRACT FROM AUTHOR]

We introduce and examine two new subclass of bi-univalent function Σ , defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers. [ABSTRACT FROM AUTHOR]

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ * : = { ϑ ∈ C : 0 < | ϑ | < 1 } by making use of the Erdély–Kober operator I ς , ϱ τ , κ which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far. [ABSTRACT FROM AUTHOR]

Under this article, we familiarize a combined class of spiral-like functions Pγ℘(β, $, ω) using the convolution product and acquire the coefficient bounds and extreme points. In addition, the findings of an integral transform, integral means inequalities and subordination are discussed. [ABSTRACT FROM AUTHOR]

In this existing paper, it is aimed to set up bonds among diverse subclasses of harmonic univalent functions by implementing specific convolution operator including Pascal Distribution Series. To be more accurate, we research this kind of relations with Goodman-Rønning type harmonic univalent functions in the open unit disc. [ABSTRACT FROM AUTHOR]

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have been attained for the function f − 1. Further application of our outcomes to certain functions demarcated by convolution products with certain normalized analytic functions in the open unit disk are specified, and we obtain Fekete–Szegö variations for this new function class defined over Poisson and Borel distribution series. [ABSTRACT FROM AUTHOR]