Mathematica Moravica, Vol. 30, No. 2 (2026)

Prathviraj Sharma, Srikandan Sivasubramanian
Estimation of coefficients for bi-Bazilevič functions with bounded boundary rotation through the application of the Faber polynomial
Mathematica Moravica, Vol. 30, No. 2 (2026), 1–13.
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Abstract. In this article, we introduce a new subclass, referred to as $\mathcal{B}_{\Sigma}(\vartheta,\lambda;\delta)$, of bi-Bazilevi\v{c} type with bounded boundary rotation. Through the application of Faber polynomials, we investigate the coefficient estimate $|g_{m}|$ for the functions in this subclass. Additionally, we derive the initial estimates for the coefficients $|g_2|$ and $|g_3|$, and we calculate the Fekete-Szegö functional $|g_{3}-\aleph g_{2}^{2}|$ for this subclass. The results presented in this paper would improve some recent works of several earlier authors.
Keywords. Bi-univalent functions, Bi-Bazilevič functions, Faber polynomial, Bounded boundary rotation expansion.

Dragana Nedić, Ismet Kalčo, Goran Cvjetković
Regularized traces of $D_{1}^{2}$ type Sturm-Liouville operators with homogeneous delay
Mathematica Moravica, Vol. 30, No. 2 (2026), 15–24.
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Abstract. The paper considers a special case of the operator $D^{2}=D^{2}(h,H,q,\alpha)$, $h,H\in R$, $q(x)\in L_{2}[0,\pi]$, operator $D_{1}^{2}$ with boundary conditions $y(0)=0$, $y'(\pi)+Hy(\pi)=0$, $(h=\infty,\; H\in R\setminus\{0\})$. Presentation of characteristic functions in two ways from the direct problem, through transformations of multiple integral and the introduction of transition functions, as well as the of characteristic functions via infinite products according to Hadamard's factorization theorem enabled the calculation of the first regularized traces.
Keywords. Regularized traces, Homogeneous delay, Characteristic function.