Search

This study aims to obtain a lower bound on the eigenvalue of the smallest modulus in a general weighted regular Sturm-Liouville problem with mixed boundary conditions. The problem is expressed as -u′′(x) + q(x)u(x) = λr(x)u(x) over the interval [a,b] with u′(a) = u(b) = 0. In 1988 Mingarelli [31]...

In this dissertation we obtain quasi-deformations of the special linear Lie algebra of degree 2 over a eld F, abbreviated sl2(F). We take F to be a eld of characteristic zero. Our approach involves obtaining and deforming a linear operator representation of sl2(F) using-twisted derivations (with...

In this thesis, we recall three types of convexities in metric spaces, namely; Menger convexity, Takahashi convexity andM-convexity. We then generalise these convexities to the framework of T0-quasi-metric spaces. Since the concept of convexities heavily relies on the concept of betweenness, a...

The concept of hyperconvexity in metric spaces was introduced by Aronszajn and Panichpakdi in 1956. This concept was then generalised to the framework of quasi-metric spaces by John Isbell in 1964, which he called Isbell convexity. In 2019, Yi git and Efe generalised this concept of...

A commutatively ordered Banach algebra (COBA) is a complex unital Banach algebra A containing a subset C, called an algebra c-cone, such that C contains the unit of A and is closed under addition, positive scalar multiplication and multiplication by commuting positive elements. If the...

The contemporary smooth structures that describe the motion of particles on underlying sets through the related specified differential geometry need to be assessed in the sense of stabilising the advantage of working with one or another. Such a study is what we call a comparative smootheology. A...

An extended quasi-metric q on a nonempty set X without any assumed structure is a distance functional that satis es the usual properties of a quasi-metric except that it can assume values of in nity, in addition to non-negative real values. Given a quasi-metrizable space X we exhibit a universal...

Given a set, the Sikorski differential space structure is determined on it by a collection of real-valued functions, while the Frölicher (smooth) structure is defined by a pair of paths into along with real-valued functions which fulfil specified sets of axioms. According to A. Batubege and P....

Given a set, the Sikorski differential space structure is determined on it by a collection of real-valued functions, while the Frölicher (smooth) structure is defined by a pair of paths into along with real-valued functions which fulfil specified sets of axioms. According to A. Batubege and P....