Generalized Analytic Function Classes Using an Extended Two-Factor q-Differential Operator: Fekete–Szegő Problem

Fekete–Szeg ˝o and Second Hankel Determinant Problems for a Bounded-Second-Derivative Class of Univalent Functions, and Its Fractional-Derivative Extension

Fractional elementary symmetric functions and Hessian estimates in the plane

We prove an endpoint Pucci maximum principle for domains in $\mathbb R^2$, formulated using a generalization of elementary symmetric polynomials to noninteger orders. As a result, we sharpen an earlier result of Astala, Iwaniec and Martin, and deduce a new Sobolev inequality for $q$-Hessians where $1<q<2$. The fraction...

Fractional q-Starlikeness in Mittag–Leffler and Limaçon Domains

In this paper, we use a normalized fractional q-derivative operator, constructed by combining Jackson’s q-difference operator with a fractional q-integral, to introduce two subclasses of normalized analytic functions in the open unit disk whose fractional transforms are starlike and univalent. The first subclass, Sq,λ*...

Geometric Properties, Partial Sums, and Fekete–Szegö Inequalities for a Normalized Four-Parameter Le Roy-Type q-Mittag–Leffler Function

In this paper, we introduce and study a normalized four-parameter Le Roy-type q-Mittag–Leffler (LR-q-ML) function defined by means of the q-Pochhammer symbol, the q-Gamma function, and the q-factorial, whose parameters directly influence the associated coefficient sequence and its growth behavior. We establish monotoni...

Local spectral analysis of class wF(p, r, q) operators via Dunford property theory

This paper investigates the local spectral properties of class (w mathcal{F}(p,r,q)\) operators. By establishing connections with a related operator-equation framework, we show that these operators satisfy important spectral properties, including the single-valued extension property (SVEP), property ((mathcal{Q})), and...

Quantum Calculus Meets Toeplitz: Sharp Bounds for p-Valent Ma-Minda Classes

In this paper, we investigate Toeplitz determinants associated with subclasses of p-valent q-starlike and q-convex Ma-Minda functions defined via the Jackson q-derivative operator. By employing subordination techniques together with coefficient estimates for functions having positive real part, we derive upper bounds f...