We have considered a fractional integral operator in this study. By using this integral operator we obtained a Briot-Bouquet superordination and sandwich theorem.
By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
We define a new class of multivalent meromorphic functions using the generalised hypergeometric function. We derived this class related to conic domain. It is also shown that this new class of functions, under certain conditions, becomes a class of starlike functions. Some results on inclusion and closure properties are also derived.
In this paper, we study Tsallis' fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs) are illustrated to recognize the accuracy of CNNs.
By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality, growth theorems, and extreme points.
The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order.
Within the scope of this research, we introduce a novel category of bi-univalent functions. Horadam polynomials are utilized to characterize these functions by utilizing series from the Poisson distribution of the Miller-Ross type. Functions from these new categories have been used to construct estimates for the Fekete-Szego functional, as well as estimates of the Taylor-Maclaurin coefficients |l2| and |l3|. These projections were created for the methods in each of these brand-new subclasses. We made some additional discoveries after, focusing on the traits that contributed to our initial findings.
The study of holomorphic functions has been recently extended through the application of diverse techniques, among which quantum calculus stands out due to its wide-ranging applications across various scientific disciplines. In this context, we introduce a novel q-differential operator defined via the generalized binomial series, which leads to the derivation of new classes of quantum-convex (q-convex) functions. Several specific instances within these classes were explored in detail. Consequently, the boundary values of the Hankel determinants associated with these functions were analyzed. All graphical representations and computational analyses were performed using Mathematica 12.0.•These classes are defined by utilizing a new q-differential operator.•The coefficient values | a i | ( i = 2 , 3 , 4 ) are investigated.•Toeplitz determinants, such as the second T 2 ( 2 ) and the third T 3 ( 1 ) order inequalities, are calculated.