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In this paper, we define a class of analytic functions, ℱ(ℋ, α, δ, µ), satisfying the following condition

By making use of the both Mittag-Leffler and Wright function, we establish a new subfamily of the class Sϑ of ϑ-spirallike functions. The main object of the paper is to provide sufficient conditions for a function to be in this newly established class and to discuss subordination outcomes. [ABSTRACT FROM AUTHOR]

In this work, bi-univalent functions, which are one of the most important research areas of Geometric Function Theory and which are still very popular in recent years, have been investigated. For the studies of functions, it is customary to determine the bound. In this direction, firstly, we introduce a new subclass of bi-univalent functions in the open unit disk D = {z ∈ C: /z/ < 1}. For this purpose, the Komatu integral operator developed for complex functions and subordination princible are used. Afterwards, the relation between the Fibonacci number sequence and the functions with the positive real part is given. This relation is a fundamental role for Results section. The upper bounds of the first two Taylor-Maclaurin coefficients are investigated. Finally, we derive Fekete-Szegö inequalities for functions belonging to this newly-defined class. The obtained results are compared with studies in the literature. [ABSTRACT FROM AUTHOR]

In this current study, by using the Pascal type distribution series of the form we define two power series and Afterwards, we develop sufficient conditions for these series to be in the class USTN(β) of analytic functions. [ABSTRACT FROM AUTHOR]

The motivation of this paper is to introduce and study a new class of univalent functions equipped with conic type regions. We also investigate a number of useful properties of this class and coefficient estimates for functions. Several consequences of the results are also pointed out. [ABSTRACT FROM AUTHOR]

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In this present investigation, by using the Horadam polynomials, we aim to build a bridge between the theory of geometric functions and that of special functions, which are usually considered very different fields. Thus, we introduce some new classes of bi-univalent functions defined by combining the q-derivative operator and the Horadam polynomials. Afterwards, we derive coefficient inequalities and consider the classical Fekete-Szegö problem. [ABSTRACT FROM AUTHOR]

In this investigation, by using a relation of subordination, we define a new subclass of analytic bi-univalent functions associated with the Fibonacci numbers. Moreover, we survey the bounds of the coefficients for functions in this class. [ABSTRACT FROM AUTHOR]

In this present investigation, we are concerned with the class O m,k S;µ,b C 0 (a) of bi-concave functions defined by using the generalized Srivastava-Attiya operator. Moreover, we derive some coefficient inequalities for functions in this class. [ABSTRACT FROM AUTHOR]

In this present investigation, we introduce the new class ... of biunivalent functions defined by using the Tremblay fractional derivative operator. Additionally, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient /an/ of the bi-univalent function class. [ABSTRACT FROM AUTHOR]

We want to remark explicitly that, by using the Ln(x) functions (essentially linked to Lucas polynomials of the second kind), our methodology builds a bridge, to our knowledge not previously well known, between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, also making use of the differential operator Ik p;q, we introduce a new class of analytic bi-univalent functions. Coefficient estimates, Fekete-Szego inequalities and several special consequences of the results are obtained. [ABSTRACT FROM AUTHOR]

In the present paper, by using the Lp,q,n(x) functions, our methodology intertwine to yield the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, we aim at introducing a new class of biunivalent functions defined through the (p, qJ-Lucas polynomials. Furthermore, we derive coefficient inequalities and obtain Fekete-Szego problem for this new function class. [ABSTRACT FROM AUTHOR]

By making use of the principle of subordination, we investigate a certain subclass of analytic functions. Such results as subordination and superordination are given. The related sandwich-type results are also presented. [ABSTRACT FROM AUTHOR]

Making use of the λ-pseudo- q -differential operator, we aim to investigate a new, interesting class of bi-starlike functions in the conic domain. Furthermore, we obtain certain sharp bounds of the Fekete–Szegö functional for functions belonging to this class. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general subclass H∑(β) of ∑m consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disc U. An estimate for the second Hankel determinant for m-fold symmetric bi-univalent functions are determined. [ABSTRACT FROM AUTHOR]

We construct two new subclasses of univalent functions in the open unit disk U = fz : jzj < 1g. For the first class $(ß) of Salagean type -pseudo-starlike functions, using the sigmoid function, we establish upper bounds for the initial coefficients of the functions in this class. Furthermore, for the second class $ we obtain Fekete{Szegffio inequalities. The results presented in this paper generalize the recent work of Babalola. [ABSTRACT FROM AUTHOR]

In this paper, we have constructed subclasses of bi-univalent functions associated with λ-bi-pseudo-starlike functions in the unit disc U. Furthermore we established bound on the coe-cients for the subclasses Sλ Σ(k;α ) and Sλ Σ (k;βfi): [ABSTRACT FROM AUTHOR]

The author constructs a new class Sqλ (G, s, t) of univalent functions applying the Ruscheweyh derivative. Moreover, the coefficient estimates including a Fekete-Szego inequality of this class were determined. [ABSTRACT FROM AUTHOR]

In this paper we introduce a class fm,kμ,bC0(β) of concave functions by using the generalized Srivastava-Attiya operator. Also, we get distortion bounds for this class. [ABSTRACT FROM AUTHOR]

In the present paper, new subclasses of bi-univalent functions of complex order associated with the (p,q)-derivative are introduced. Furthermore, using the Faber polynomial expansions, we get upper bounds for the coefficients of functions belonging to these classes. [ABSTRACT FROM AUTHOR]

We study a newly constructed subclass of bi-univalent functions. Furthermore, we establish Chebyshev polynomial bounds for the coefficients, and Fekete-Szegö inequality, for the class Sσ(μ, t) [ABSTRACT FROM AUTHOR]

In this work, we introduce two new subclasses SΣm(α,λ) and SΣm(β,λ) of Σm consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disc U. Furthermore, for functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for ∣αm+1∣ and ∣α2m+1∣. [ABSTRACT FROM AUTHOR]

In this paper we study the class C0(α)(α∈(1,2]) - the class of the so-called concave univalent functions. The main aim is to obtain an upper bound to the third Hankel determinant for concave univalent functions. [ABSTRACT FROM AUTHOR]

In this paper we discuss some newly constructed subclasses of bi-univalent functions and establish bounds for the coefficients of the functions in the subclasses SΣ(λ,α) and SΣ(β). [ABSTRACT FROM AUTHOR]