In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

For Jacobi matrices with an 1⁄4 1þ ð 1Þan g; bn 1⁄4 ð 1Þbn g; we study bound states and the Szeg + o condition. We provide a new proof of Nevai’s result that if g4 2 ; the Szeg + o condition holds, which works also if one replaces ð 1Þ by cos ðmnÞ: We show that if a 1⁄4 0; ba0; and go1 2 ; the Szeg + o condition fails. We also show that if g 1⁄4 1; a and b are small enough (b þ 8a2o 1 24 will d...

Abstract. In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szeg ́́...

Let e ⊂ R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szeg˝ o condition is equivalent to lim sup a 1 · · · a n cap(e) n > 0 (this includes prior results of Widom and Peherstorfer–Yuditskii). Using Remling's extension of the Denisov–Rakhmanov theorem and an analysis of Jos...

We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain $\mathbb{R}^2$. Motivated by geometric inequalities, we prove non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out be very robust and allows for simple proof Szeg\"o type inequality as well new reformulation Faber-Krahn ...

With s n (z) denoting the n-th partial sum of e z , the exact rate of convergence of the zeros of the normalized partial sums, s n (nz), to the Szeg} o curve D 0;1 was recently studied by Carpenter et al. (1991), where D 0;1 is deened by

In this paper, we establishes certain new weighted Young and P?lya-Szeg?-type inequalities involving Marichev-Saigo-Maeda fractional integral operators. Meanwhile, corresponding Cauchy-Schwarz type inequalities, Shisha-Mond Diaz-Metcalf for operators are also obtained. As applications, some estimates Chebyshev-type with two unknown functions presented. The main results of paper more general inc...

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.