International Journal of Open Problems in Computer Science and Mathematics

Estimation of Radii of Regions of Starlikeness and Spirallikeness for Analytic Mappings

2026-01-14T07:39:18+00:00

Many researchers in complex analysis have invested time particularly in investigating geometric properties like starlikeness and spirallikeness of analytic mappings on the unit disk. Finding the exact lengths of the radii in the starlike and or spirallike regions for these functions is very difficult since these shapes are not regular. This therefore requires that an estimation of the radii of these regions be carried out. This research seeks to estimate the radii within which analytic mappings in the unit disk remain starlike or spirallike. This note derives sharp radii estimates and constructs extremal functions achieving these estimates. The methodology involved using techniques of differential subordination, coefficient estimates, distortion theorems, and subordination principles. Moreover, algorithm development techniques were used as well as numerical methods to come up with pictorial representation of starlikeness and spirallikeness regions. Advancement of theoretical development of geometric function theory and also in providing sharp radii bounds useful in modeling involving conformal maps which enhances applications in engineering, fluid dynamics, and signal theory requires the results generated in this work.

Mixed SuperHyperStructure and Some Open Problems

2026-01-25T00:17:14+00:00

Hyperstructures extend classical algebraic systems by allowing operations to return sets of possible results rather than single outputs. Iterating this idea across multiple layers of collections gives rise to superhyperstructures, which provide a natural framework for describing hierarchical and multilevel interactions. This work introduces two mixed higherorder frameworks: Mixed HyperStructures and Mixed SuperHyperStructures. In addition, I have included several open problems at the end of this paper.

Introducing a new tangent distribution

2026-03-29T13:31:15+00:00

To date, only a limited number of basic unit distributions based on the tangent function have been considered. In this article, we expand this range by introducing a new candidate distribution and examining its key probabilistic properties, such as the cumulative distribution function, probability density function, quantile function, and moments. Particular emphasis is placed on analytical tractability. While potential applications fall outside the scope of this study, they could be investigated by specialists in relevant fields. Additionally, we highlight an open problem regarding the rigorous derivation of the second-order moment, which could stimulate further theoretical research.

On Certain properties of Finite Rank Operators and Bishop-Phelps-Bollobas Criterion in Banach Spaces

2026-02-04T02:23:01+00:00

For bounded linear operators, it is observed that, Bishop-Phelps-Bollobas criterion has not been studied when operators are of finite rank exhaustively. Therefore, it is an area of interest in the concept of denseness of norm achieving mappings to determine whether every finite rank operator between Banach spaces can be estimated by those that achieve their norms. Hence, it has not been shown whether the set of norm achieving finite rank operators is dense in the whole space of mappings of finite rank. We analyzed this properties particulary norm-attainability. We showed that rank one mappings achieve their norms on certain Banach lattices. Since finite rank operators are obtained by summing rank one mappings, our results seeks to clarify the behavior of such operators especially in relation to norm-attainability and operator structure with regard to Bishop-Phelps-Bollobas property.

Short Introduction to SuperHyperGraph Theory with some applications

2026-03-12T15:42:38+00:00

A finite hypergraph extends an ordinary graph by permitting each hyperedge to connect an arbitrary nonempty subset
of vertices, thereby encoding genuinely multiway interactions. Building on this idea, a finite SuperHyperGraph is formed by iterating the powerset construction, so that set-valued objects created at one level can act as vertices (and hence as potential edge endpoints) at the next. This provides a principled framework for representing hierarchical, nested, and multilayer relational structures. In this paper, we introduce SuperHyperGraphs and several related concepts, illustrating them with concrete examples.