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In this review, we started by considering a normed space , its dual and bi-dual spaces. We define functionals on , as those functionals that are bounded linear functionals and then establish a corresponding unique bounded linear functional that defines a canonical mapping of into such that is linear, injective and preserves norm. By this, isomorphism is established so that reflexive maps are realized. In the cause of this work, we invoked the idea of compact topological space and operators mapped on them. We also discussed separable spaces as it relates to this topic. The work was rounded up in section three by discussing the Tychonoff’s theorem as it relates to the weak topology in conjugate spaces, adjoint operators and conjugate spaces of and .
Ukpong K. Undergraduate real analysis lecture notes. Federal University of Technology, Yola, Nigeria; 1987.
Vatsa BS. Principles of mathematical analysis. CBS Publishers & Distributors, New Delhi, India; 2002.
Charles E. Chidume. functional analysis (An introduction to metric spaces) Longman, Nigeria; 1989.
Chika Moore. Lecture notes on advance linear functional analysis. Nnamdi Azikiwe University, Awka, Nigeria; 2001.
Charles Chidume, Springer-Verlag London Limited; 2009.
Chidume C.E, Chidume C.O. Foundations of riemann integration (Monograph). The Abdusalam International Center for Theoretical Physics, Trieste, Italy; 2003.
Chidume CE. An iterative process for nonlinear lipschitzian strongly accretive mapping in L^p Spaces” Journal of Mathematical Analysis and Applications. 1990;152:2 453-461.
Steven G. Krantz. Real analysis and foundations. Chapman & Hall CRC; 2010.
William F. Trench. Instructors solution manual introduction to real analysis. National Mathematical Center, Abuja, Nigeria; 2010.
Atkin RJ, Fox N. An introduction to the theory of elasticity. Longman, London and New York; 1980.
Charles E. Chidume, Mbaro-Saman Lubuma. Solution of the stokes system by boundary integral equations and fixed point iterative schemes. Journal of the Nigerian Mathematical Society. 1992;2(3): 1-17.
Royden HL. Real analysis, Prentice Hall of India, New Delhi, India; 2008.
Chidume CE. Foundation of Mathematical analysis. The Abdusalam ICTP, Trieste, Italy; 2006.
Ioannis K. Argyros. Approximate solution of operator equations with applications. World Scientific Publishing Co. Plc Ltd; 2005.
Frigyes Riez, Belasz Nagy. Functional analysis dover publications, Inc. New York; 1990.
Mieczyslaw Altman. Contractors and contractor directions theory and applications (A new approach to solving equations). Marcel Dekker Inc. New York and Basel; 1977.
Ejike UBCO. A postgraduate lecture note in functional analysis. Federal University of Technology Owerri, Nigeria; 1991.
Avner Friedman. Foundations of modern analysis. Dover Publications, Inc. New York; 1982.
Chidume CE. Approximation of fixed points of Quasi-contractive mappings in L^p Spaces” Indian Journal of Pure and Applied Mathematics 22. 1991;1:273- 281.
Rama B. Bhat, Rao V. Dukkipati. Advanced dynamics Narosa Publishing House, New Delhi; 2005.