In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This utilized to develop new subfamilies of bi-univalent via principle subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on estimation coefficients |a?|(?=2,3) Fekete–Szegö inequality for belonging these...

For r > 0 let r {z ∈ : |z| < r}. Let 1 . Let the functions f and F be analytic in the unit disc . A function f is called subordinate to F, written f ≺ F, if F is univalent in , f 0 F 0 and f ⊂ F . Let D be a domain in 2 and ψ : 2 ⊃ D → be an analytic function, and let p be a function analytic in with p z , zp′ z ∈ D, z ∈ and h be a function analytic and univalent in . The function p is said to ...

In the present paper, a general subclass Mh,p ?m (?, ?) of m-Fold symmetric bi-univalent functions is de?ned. Also, estimates TaylorMaclaurin coefficients |am+1|, |a2m+1| and Fekete-Szegö problems are obtained for in this new subclass. The results presented paper would generalize improve some recent works several earlier authors.

The interplay of geometry and analysis is perhaps the most fascinating aspect of complex function theory. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior. A function is said to be univalent (or schlichi) if it never takes the same value twice: f(z{) # f(z2) if zx #= z2. The present survey will focus upon the class S ...

In this work, we investigate the (p, q)-Gegenbauer polynomials for a class of analytic and bi-univalent functions defined in open unit disk, with respect to subordination. We give an elementary proof establish some estimates coefficient bounds new class. conclude study by giving result Fekete-Szegö theorem. A corollary was given show results subclasses our

In the present paper, we investigate two new subclasses 〖AR〗_(Σ_m ) (δ,λ;α) and (δ,λ;β) of Σ_m consisting m-fold symmetric holomorphic bi-univalent functions in open unit disk Δ. For from classes described here, obtain estimates on initial bounds |d_(m+1) | |d_(2m+1) |. addition, get special cases for our results.

In this study, a new class RΣμ(x,γ,α,δ,β) of bi-univalent functions studied by means Gegenbauer polynomials (GP) with Rabotnov is introduced. The coefficient the Taylor coefficients a2 and a3 Fekete-Szegö problems for belonging to have been derived as well. Furthermore, variety results will appear considering parameters in main results.

Clostridial and spinach ferredoxins, reduced enzymatically by the action of ferredoxin-TPN+ oxidoreductase, have been shown to carry out the univalent reduction of oxygen. The superoxide radicals, so generated, were detected by their ability to cause the oxidation of epinephrine to adrenochrome. Superoxide dismutase prevented the production of adrenochrome in these reaction mixtures, while havi...