Pure and Applied Mathematics
http://repository.aust.edu.ng/xmlui/handle/123456789/442
This collection contains master's Theses of Pure and Applied Mathematics from 2009 to 2022.Sun, 13 Oct 2024 07:14:35 GMT2024-10-13T07:14:35ZThe Auman Integral of Set-Valued Maps
http://repository.aust.edu.ng/xmlui/handle/123456789/5136
The Auman Integral of Set-Valued Maps
Eleh, Chinedu Anthony
This thesis focuses on the Aumann integral of set-valued random variables and its properties. We started o by studying the space in which this integral lies: hyperspace endowed with the Hausdor metric. We considered convergence on a hyperspace with respect to the Hausdor metric and reviewed the works of Kuratowski, Mosco in trying to abstract topologically, the Hausdor convergence; this led to a comparison between weak, Wijsmann, Kuratowski-Mosco convergences to Hausdor convergence. We proceeded to see the conditions under which a set-valued random variable is measurable, integrable and integrably bounded. Finally, we de ned the class of integrable selections of an integrable set-valued random variable and used it to de ne the Aumann integral, and went further to prove and outline su cient conditions for the Aumann integral to be convex and closed-valued respectively
Main Thesis
Tue, 15 May 2018 00:00:00 GMThttp://repository.aust.edu.ng/xmlui/handle/123456789/51362018-05-15T00:00:00ZCo−Semigroups of Contradiction on Banach Spaces and Applications
http://repository.aust.edu.ng/xmlui/handle/123456789/5126
Co−Semigroups of Contradiction on Banach Spaces and Applications
Isedowo, Joshua Wale
Let X be a Banach space and A : D(A) ⊂ X −→ X be an unbounded linear operator on X. We study the concept of C0−semigroup of contraction on arbitrary Banach space X and give the two characterizations of A called infinitesimal generator of C0−semigroup on X namely, Hille-Yosida and Lumer Phillips characterizations. In the later part, we apply the approach of C0−semigroups to some partial differential equations with boundary conditions.
Main Thesis
Fri, 17 Mar 2023 00:00:00 GMThttp://repository.aust.edu.ng/xmlui/handle/123456789/51262023-03-17T00:00:00ZMeasurable Set-Valued Functions and Bochner Integrals
http://repository.aust.edu.ng/xmlui/handle/123456789/5125
Measurable Set-Valued Functions and Bochner Integrals
Eze, Leonard Chidiebere
In this thesis, several concepts from Topology, Measure Theory, Probability Theory, and Functional analysis were combined in the study of the measurability of set-valued functions and the Bochner integral. We started with a detailed study of the Hausdorff metric, its properties, and topology by exposing separately the case where E is a metric space and the case where E is a normed linear space. After reviewing the important theorems, we present the four convergences related to Hausdorff metric: Hausdorff convergence,
Wisjman convergence, Weak convergence, and Kuratowski-Mosco convergence; and then compared them. Further, set-valued random variables and their properties were studied. We study and compare five types of measures of set-valued functions and the two forms of Bochner integral, that is, the Banach-valued and set-valued Bochner integrals.
Tue, 12 Dec 2017 00:00:00 GMThttp://repository.aust.edu.ng/xmlui/handle/123456789/51252017-12-12T00:00:00ZA Measure Theory and Integration Approach to Probability Theory, and Applications in Financial Markets (Black-Scholes model), and Actuarial Mathematics (Ruin Probability)
http://repository.aust.edu.ng/xmlui/handle/123456789/5079
A Measure Theory and Integration Approach to Probability Theory, and Applications in Financial Markets (Black-Scholes model), and Actuarial Mathematics (Ruin Probability)
Nwonu, Blessing Uchenna
2021 Pure and Applied Mathematics Masters theses
Thu, 10 Jun 2021 00:00:00 GMThttp://repository.aust.edu.ng/xmlui/handle/123456789/50792021-06-10T00:00:00Z