On Review of the Riemanns’ Iterated Integrals


Published: 2019-11-27

Page: 33-50

Eziokwu, C. Emmanuel *

Department of Mathematics, Micheal Okpara University of Agriculture, Umudike, Abia State, Nigeria.

*Author to whom correspondence should be addressed.


This paper reviews the Riemanns’ approach of multiple integrals by considering its basic definitions, results and the various successive integral evaluations, in doing this, the continuity condition of R was considered with respect to X as the necessary condition guaranteeing the existence of the integrals using the analytical Riemanns’ approach. This involves the use of partitions, to generate continued results to the nth iterated integral after the nth iteration.

Keywords: Riemanns’ sum, function, supremum, infimum, continuity, Riemanns’ integrability and iterated integrals.

How to Cite

Emmanuel, E. C. (2019). On Review of the Riemanns’ Iterated Integrals. Asian Journal of Pure and Applied Mathematics, 1(1), 33–50. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/796


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Vatsa BS. Principles of mathematical analysis. CBS Publishers & Distributors, New Delhi, India; 2002.

Abdul Hassan Siddiqi. Applied functional analysis. A Dekker Series of Monographs and Textbooks, New Brunsvaleki New Jersey; 2008.

Rama B. Bhat, Rao V. Dukkipati. Advanced dynamics. Narosa Publishing House, New Delhi; 2005.

Frigyes Riez, Belasz Nagy. Functional analysis. Dover Publications, Inc. New York; 1990.

Avner Friedman. Foundations of Modern Analysis. Dover Publications, Inc. New York; 1982.

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.

Chidume CE. Approximation of fixed points of quasi-contractive mappings in L^p spaces. Indian Journal of Pure and Applied Mathematics. 1991;22(1):273-281.

Steven G. Krantz. Real analysis and foundations. Chapman & Hall CRC; 2010.

Chidume CE. Foundation of mathematical analysis. The Abdusalam ICTP, Trieste, Italy; 2006.

Chidume CE, Chidume CO. Foundations of riemann integration (Monograph). The Abdusalam International Center for Theoretical Physics, Trieste, Italy; 2003.

William F. Trench. Instructor’s solution manual introduction to real analysis. National Mathematical Center, Abuja, Nigeria; 2010.

Charles E. Chidume. Functional analysis (An Introduction to Metric Spaces). Longman, Nigeria; 1989.

Charles E. Chidume, Mbaro-SamanLubuma. 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.

Charles Chidume. Springer-Verlag London Limited; 2009.

Chika Moore. Lecture notes on advance linear functional analysis. Nnamdi Azikiwe University, Awka, Nigeria; 2001.

Erwin Kreyzig. Introductory functional analysis with applications. John Wiley and Sons, New York; 1978.

Royden HL. Real analysis. Prentice Hall of India, New Delhi, India; 2008.

Ioannis K. Argyros. Approximate solution of operator equations with applications. World Scientific Publishing Co. Plc Ltd; 2005.

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.

William F. Trench. Introduction to real analysis. National Mathematical Center Abuja, Nigeria; 2010.

Ukpong K. Undergraduate real analysis lecture notes. Federal University of Technology, Yola, Nigeria; 1987.

Atkin RJ, Fox N. An introduction to the theory of elasticity. Longman, London and New York; 1980.