By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete–Szegö-type inequalities for functions in each of these subclasses are obtained. The results derived in this article are shown to extend and generalize those in some earlier works.

/pdf/applications-of-the-q-derivative-operator-to-new-families-of-3byre8pi.pdf

Applications of the q-Derivative Operator to New Families of Bi-Univalent Functions Related to the Legendre Polynomials

Some subclasses of p-valent 
 
 
 
 $$\gamma $$
 
 γ
 
 -uniformly type q-starlike and q-convex functions defined by using a certain generalized q-Bernardi integral operator

In the present paper, we consider a subclass of starlike functions G3/2 defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the bounds of Fekete–Szegö-type inequalities and Hankel determinants for functions in this class. It is proved that maxH3,1(f):f∈G3/2 is equal to 181. The bounds for f∈G3/2 are sharp.

/pdf/certain-sharp-coefficient-results-on-a-subclass-of-starlike-2o1vhjbp.pdf

Certain Sharp Coefficient Results on a Subclass of Starlike Functions Defined by the Quotient of Analytic Functions

One of the most important problems in the study of geometric function theory is knowing how to obtain the sharp bounds of the coefficients that appear in the Taylor–Maclaurin series of univalent functions. In the present investigation, our aim is to calculate some sharp estimates of problems involving coefficients for the family of convex functions with respect to symmetric points and associated with a hyperbolic tangent function. These problems include the first four initial coefficients, the Fekete–Szegö and Zalcman inequalities, and the second-order Hankel determinant. Additionally, the inverse and logarithmic coefficients of the functions belonging to the defined class are also studied in relation to the current problems.

/pdf/results-on-second-order-hankel-determinants-for-convex-1kjsa1mo.pdf

Results on Second-Order Hankel Determinants for Convex Functions with Symmetric Points

Sharp Bounds of Hankel Determinant for the Inverse Functions on a Subclass of Bounded Turning Functions

In the present paper, we aimed to discuss certain coefficient-related problems for the inverse functions associated with a bounded turning functions class subordinated with the exponential function. We calculated the bounds of some initial coefficients, the Fekete–Szegö-type inequality, and the estimation of Hankel determinants of second and third order. All of these bounds were proven to be sharp.

/pdf/results-on-hankel-determinants-for-the-inverse-of-certain-25wgsb88.pdf

Muhammad Ihsan

Papers

Results on Hankel Determinants for the Inverse of Certain Analytic Functions Subordinated to the Exponential Function

Sharp Bounds of Hankel Determinant for the Inverse Functions on a Subclass of Bounded Turning Functions