Browsing by Author "Musundi Sammy Wabomba"

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Correspondence of Fixed-Point Theorem in � �𝟐, 𝑻𝟑 − 𝑺𝑷𝑨𝑪�
(Asian Research Journal of Mathematics, 2024-08-19) Amos Koros; Musundi Sammy Wabomba; Mark Okongo
Fixed-point theory (FPT) has lot of applications not only in the field of mathematics but also in various other disciplines. Fixed Point Theorem presents that if 𝑇: 𝑋 → 𝑋 is a contraction mapping on a complete metric space (𝑋, 𝑑) then there exists a unique fixed point in 𝑋. FPT is also essential in game theory, in this case Brower Fixed Point has an application in game theory specifically in non-cooperative games and existence of Equilibrium. In particular, a game is a set of actions done by the participants defined by a set of rules. This is commonly described using mathematical concepts, which offers a concrete model to describe a variety of situations. On the other hand, the separation axioms 𝑇𝑖, 𝑖 = 0,1,2,3,4 are vital properties that describes the topological spaces 𝑇0 , 𝑇1 , 𝑇2, 𝑇3 and 𝑇4 . It is noted that a 𝑇3 − 𝑠𝑝𝑎𝑐𝑒 is a generalized version of 𝑇2-space and since various results on application of fixed point theory in game theory on an arbitrary locally convex � �2 − space has been established, in this study we sort to extend this concept to the general 𝑇3 − 𝑠𝑝𝑎𝑐𝑒. The utilization of a symmetric property of Hausdorff space established that if two continuous commutative mappings are defined on a 𝑇3 − 𝑠𝑝𝑎𝑐𝑒, then the two maps achieves unique fixed points.
Properties of Isosceles, Pythagorean and Isosceles-Pythagorean Vectors in the Characterization of Hilbert Spaces
(Asian Journal of Pure and Applied Mathematics, 2024-11-05) Damaris Njeri Mugure; Musundi Sammy Wabomba; Alice Lunani Murwayi
All Hilbert spaces are Banach spaces but the converse is not necessarily true. Characterization of Banach spaces as Hilbert spaces has had different approaches for various Banach spaces. It has been shown that a separable Banach space which is almost transitive with vector orthogonalities for dimension greater than three is a Hilbert space. It worthy to note that micro transitivity together with Isosceles (I), Pythagorean (P) and Isosceles Pythagorean (IP) orthogonalities in the unit sphere have some essential properties that can be considered in characterization of Hilbert spaces. In this study, separable micro transitive Banach spaces are examined and their characterization as Hilbert spaces is achieved by applying the I-vector property in affine sets along with the P and IP-vector properties. In particular, by letting a separable Banach space 𝑋 of 𝑑𝑖𝑚𝑋 ≥ 2 possessing micro transitivity property with I, P, and IP vectors, then 𝑋 is a Hilbert space. The results of this research are expected to be useful in algebra and differential operators, particularly for calculating wave functions and formulation of theory
Properties of Unitary Quasi-Equivalence on Isometry, Co-Isometry, and Partial Isometry Operators
(2024-04-16) Anyembe Lilian; Musundi Sammy Wabomba; Kinyanjui Jeremiah Ndung’u
The present study aims to determine the properties of unitary quasi-equivalence and isometry, co-isometry and partial isometry operators. Unitary quasi- equivalence has been shown to be an equivalence relation. Similarly, unitary quasi-equivalence has been proven to preserve normality, hyponormality and binormality of operators. However, the properties of unitary quasi-equivalence and partial isometric operators have not been established. Based on the preceding results, it establishes that unitary quasi-equivalent operators preserve; isometry, co-isometry and partial isometric properties.