JAEM 2025, Vol 15, No 7

Estimates of Toeplitz determinants for certain subclasses of bi-univalent function related to modified sigmoid function

Tue, 01 Jul 2025 00:00:00 GMT

Estimates of Toeplitz determinants for certain subclasses of bi-univalent function related to modified sigmoid function Padmanabhan, Vijayalakshmi; Rithika J., Sree The current comprehensive study aimed to determine upper bounds of Toeplitz determinants for some subclasses of bi-univalent functions. A function f ∈ A is said to be bi-univalent in ∆ if both f and f−1 are univalent in ∆. Modified sigmoid function play an important role in Geometric function theory and in this paper we derive the Sharp coefficient estimates, Fekete-Szegö inequality, second and third order Toeplitz determinants, for the subclasses S*σ(S), Cσ(S) of bi-univalent Sakaguchi type functions associated with the modified sigmoid function.

An improvement and a generalization of Ankeny and Rivlin’s result on the maximum modulus of polynomials

Tue, 01 Jul 2025 00:00:00 GMT

An improvement and a generalization of Ankeny and Rivlin’s result on the maximum modulus of polynomials Ngamchui, Reingachan; Laishangbam, Raju; Chanam, Barchand; Thoudam, Ranaranjan For an arbitrary entire function f(z), let M(f, r) = max|z|=r|f(z)|. By considering the polynomial of degree n having no zero in the interior of the unit circle|z| = 1, Ankeny and Rivlin obtained M(p, R) ≤ Rn + 1/2 M(p, 1), R ≥ 1. In this paper, we consider the polynomial of degree n having no zero in |z| < k, k ≥ 1 and simultaneously considering the sᵗʰ derivative, 0 ≤ s < n, of the polynomial, we have obtained an improvement as well as a generalization of Ankeny and Rivlin’s result.

A study on (c, d) IF − Q uniform spectral spaces

Tue, 01 Jul 2025 00:00:00 GMT

A study on (c, d) IF − Q uniform spectral spaces Thirukumaran S.; Revathi, Govindasamy Krishnamoorthy A conceptual way of approach to sober space is explored by the irreducibility of closed sets and their components in topological spaces. Sober space has been defined by both generic points and the irreducibility of closed sets. From this, the extension of a novel space which is known as spectral space is developed. Spectral space is one of the inventive extensions of sober space. Spectral space, can also be studied along with compact spaces, T0 space and sober space in topological space. T0 space has played a major role in spectral space. Quasi-spectral space and Semi-spectral space are also probed in addition to spectral space. In this article, the author introduces a new concept called (c, d) IF − Q uniform irreducible closed set. By using it the new space called (c, d) IF − Q uniform sober space is introduced and studied. The extension of (c, d) IF – Q uniform sober space is studied as (c, d) IF − Q uniform spectral space. Moreover, (c, d) IF − Q uniform semi-spectral space and (c, d) IF − Q uniform quasi-spectral space are also introduced and some of its properties are discussed.

A study on upper deg-centric graphs

Tue, 01 Jul 2025 00:00:00 GMT

A study on upper deg-centric graphs Thalavayalil, Timmy Tomy; Kok, Johan; Sudev, Naduvath K. The upper deg-centric graph of a simple, connected graph G, denoted by Gud, is a graph constructed from G such that V (Gud) = V (G) and E(Gud) = {vivj : dG(vi, vj ) ≥ degG(vi)}. This paper introduces and discusses the concepts of upper degcentric graphs and iterated upper deg-centrication of a graph.