Functional Analysis
Associate Professor / Reader
Mathematics
At the Mathematics department office
Appointment on Visitation important
Topic: INTRODUCTION
Description:
The research work is focused on Pure Mathematics which is a branch of modern day Mathematics. The area of specialization is Functional Analysis with special interest on Fixed Point Theory in Metric, Banach and Hilbert Spaces.
AIM OF RESEARCH WORK
The aim of my research work is to introduce new extensions and generalizations to existing results in literature in the field of Fixed Point Theory. The aim of the research work is also concerned with the qualitative study on the Existence, Uniqueness, Convergence and Stability of Fixed Points in Complete Metric Spaces and Banach Spaces.
OBJECTIVES OF RESEARCH WORK
The specific objectives are to:
(i) establish some strong convergence results on Jungck-Mann and Jungck Iteration in arbitrary Banach Spaces.
(ii) use the notion of A-Distance and E-Distance as well as the notion of comparison functions to prove some stability theorems using selfmappings in uniform spaces.
(iii) employ the concept of Jungck-Noor Iteration process associated with the generalized Zamfirescu mappings to prove some fixed point results.
(iv) show the relationship between the Noor Iteration and Jungck-Noor Iteration which is an improvement over other existing results in literature in the field of Fixed Point Theory.
(v) introduce some strong convergence results for the Jungck-Ishikawa and Jungck-Mann iteration processes in Banach spaces.
(vi) prove the stability of Noor Iteration for a general class of functions in Banach Spaces. Special cases of Ishikawa and Mann Iterations were also considered for a general class of functions in the same spaces.
(vii) unify and improve some of the known stability results in literature in the field of Fixed Point Theory.
(viii) generalize and extend the stability results for asymptotically and non expansive mappings in uniformly convex Banach spaces.
CONTRIBUTIONS TO KNOWLEDGE
Some of the contributions to knowledge of this research are as follows:
(i) This research introduced the notion of the general class of mappings to prove the strong convergence results on Jungck - Mann and Jungck iterations in arbitrary Banach Spaces.
(ii) The study proved the stability of Picard and Mann iterations for a general class of functions.
(iii) This research work established the Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces.
(iv) This research used the concept of E-distance and comparison functions to prove stability theorem in Hausdorff Uniform spaces.
(v) The study established the existence and uniqueness theorems for some common fixed points in Hausdorff Uniform spaces.
(vi) This research proved convergence theorem for the general Noor iteration process in uniformly smooth Banach spaces.
(vii) The study established some generalizations of some common fixed point theorems in uniform spaces.
(viii) The study proved some results on the equivalence of implicit Kirk-Type fixed point iteration schemes for a general class of maps in Banach spaces.
# | Certificate | School | Year |
---|---|---|---|
1. | Ph.D (MATHEMATICS/FUNCTIONAL ANALYSIS) | DEPARTMENT OF MATHEMATICS, OBAFEMI AWOLOWO UNIVERSITY, ILE-IFE, NIGERIA | 2008 |
INTRODUCTION: The research work in progress is on Fixed Point Theory in complete metric and Banach spaces.
AIM: The aim of this research work is to establish the Stability of Noor Iteration for a general class of functions in Banach Spaces. The case of Noor Iteration associated with Zamfirescu mappings in uniformly convex Banach Spaces will also be deduced.
METHODOLOGY: The concept of Noor iterations associated with Zamfirescu mappings are proved as a special case. The concept of Jungck-Noor iteration process associated with the generalized Zamfirescu mappings are formulated and considered.
CONTRIBUTIONS TO KNOWLEDGE: The results obtained improve and generalize some of the known results in literature as a major contribution to knowledge in the field of Fixed Point Theory. The relationship between the Noor Iteration and Jungck-Noor Iteration also established as a contribution to the frontiers of knowledge in the field of Fixed Point Theory. Our results unify and improve some well known results in literature as well as provide a vital contribution to knowledge in the field of Fixed Point Theory.
BOSEDE ALFRED is a Associate Professor / Reader at the Department of Mathematics
BOSEDE has a Ph.D in MATHEMATICS/FUNCTIONAL ANALYSIS from DEPARTMENT OF MATHEMATICS, OBAFEMI AWOLOWO UNIVERSITY, ILE-IFE, NIGERIA