Cheng-Ming Lee's Publication List

  1. On a discrete analogue of inequalities of Opial and Yang, Canadian Math. Bull. 11(1968), 73-77.
  2. On fixed point theorems for mapping in a separated locally convex space, Canadian Math. Math. Bull. 15(1972), 603-604.
  3. On sequences of contractive-like mappings and fixed points, Comment. Math. Univ. Carolinae 13(1972), 437-444.
  4. On the integrals of Perron Type, Ph. D. thesis, University of British Columbia, Vancouver, Canada (1972).
  5. On the integrals of Perron type (with P. S. Bullen), Trans. Amer. Math. Soc. 182(1973), 481-501.
  6. The SCP-integral and the P(n+1)-integral (with P. S. Bullen), Canadian Jour. of Math. 25(1973), 1274-1284.
  7. The second approximate derivative and the second approximate Peano derivative (with R. J. O'Malley), Bull. Inst. Math. Acad. Sinica 3(1975), 193-197.
  8. On the approximate Peano derivatives, Jour. London Math. Soc. 12(1976), 475-478.
  9. An approximate extension of Cesaro-Perron integrals, Bull. Inst. Math. Acad. Sinica 4(1976), 73-82.
  10. Thermodynamics of intermetallic phases with the triple-defect B2 Structure (with J. P. Neumann and Y. A. Chang), Acta Metallurgica 24(1976), 593-604.
  11. On functions with summable approximate Peano derivatives, Proc. Amer. Math. Soc. 57(1976), 53-57.
  12. Monotonicity theorems for approximate Peano derivatives and integrals, Real Analysis Exchange 1(1976), 52-62.
  13. An observation on Neugebauer's characterization of derivatives, Real Analysis Exchange 2(1976), 40-42.
  14. A development of contraction mapping principles on Hausdorff uniform spaces, Trans. Amer. Math. Soc. 226(1977), 147-159.
  15. A note on metrically inward mappings (with K. K. Tan), Comment. Math. Univ. Carolinae 18(1977), 259-263.
  16. Generalizations of l'Hopital's rule, Proc. Amer. Math. Soc. 66(1977), 315-320.
  17. An analogue of the theorem of Hake-Alexandroff-Looman, Fund. Math. 100(1978), 69-74.
  18. An existence theorem via an intuitive idea and fixed point theorems, Comment. Math. Univ. Carolinae 19(1978), 715-725.
  19. On Fan's extensions of Browder's fixed point theorems for multi-valued inward mappings (with K. K. Tan), Australian Jour. Math. 26(1978), 169-174.
  20. On the oscillatory behavior of certain derivatives, Real Analysis Exchange 4(1979), 178-183.
  21. On integrals with summable trigonometric series, Real Analysis Exchange 4(1978/79), 66-68.
  22. On integrals and summable trigonometric series, Bull. Canadian Math. 24(1981), 433-440.
  23. Added mass of a spheroid oscillation in a stratified fluid (with R. Y. S. Lai), Int. Jour. Engrg. Sci. II(1981), 1411-1420.
  24. Generalizations of Cesaro continuous functions and integrals of Perron type, Trans. Amer. Math. Soc. 266(1981), 461-481.
  25. On Baire one Darboux functions with Lusin's condition (N), Real Analysis Exhange &(1981/82), 61-64.
  26. Regular approximate Peano derivatives are the ordinary ones, Bull. Inst. Math. Acad. Sinica 10(1982), 401-404.
  27. On generalized Peano derivatives, Trans Amer. Math. Soc. 275(1983), 381-396.
  28. On absolute Peano derivatives, Real Analysis Exchange 8(1982/83), 227-245.
  29. On generalizations of Peano derivatives and integrals - via the coefficient problems of convergent trigonometric series, Real Analysis Exchange 9(1983/84), 369-378.
  30. On Bernoulli-l'Hopital-Ostrowski's rule and monotonicity theorems, Canadian Math. Bull. 27(1984), 273-278.
  31. On generalizations of exact Peano derivatives, Contemporary Math. 42(1985), 97-103.
  32. On Lusin's condition (N) and some of its modifications, Real Analysis Exchange 13(1987/88), 151-155.
  33. Some Hausdorff variants of absolute continuity, Banach's condition (S) and Lusin's condition(N), Real Analysis Exchange 13(1987/88), 404-419.
  34. Bolyai-Gerwien theorem and Hilbert's third problem, Proc. of the Thirteenth Summer Symposium in Real Analysis, Real Analysis Exchange 15(1989/90), 44-46.
  35. A symmetric approximate Perron integral for the coefficient problem of trigonometric series, Real Analysis Exchange 16(1990/91), 429-439.
  36. Characterizations of turbulent one dimensional mappings via "w"-limit sets (with Evans, Humke and O'Malley), Trans Amer. Math. Soc. 326(1991), 261-280.
  37. The dynamics of Newton's method for functions in certain spaces, Proceeding of the Nineteenth Summer Symposium in Real Analysis (Italy). Real Analysis 21(1995/96), 43-45.

Other Works

  1. Theory of Equidecomposition, a graduate lecture note (1989), 52 pages.
  2. Newton's Method and Dynamical Systems, a seminar note (1991), 34 pages.
  3. On random tries for approximate solutions, a seminar note (1991), 3 pages.
  4. On Newton's method for polynomials of degree three and Mandelbrot sets, a seminar note (1991), 6 pages.
  5. From local stability to bad irrationals, a seminar note (1991), 3 pages.
  6. Baire's category theorem with applications, a graduate lecture note (1992), 15 pages.
  7. Unifying Newton integral and Lebesgue integral through Baire's category theorem, an expository note (1992), 4 pages.
  8. ** Mr. Jianping Yang finished his Ph. D. dissertation on "Newton's Method and Dynamical Systems" under my supervision in December, 1992. **
  9. Double and iterated limits of nets, unpublished manuscript, 11 pages, 1993.
  10. On Quantum Mechanics and Functional Analysis, a graduate lecture note (1993), 26 pages.
  11. On complete measure spaces, a graduate lecture note (1993), 4 pages.
  12. On Vitali theorem, a graduate lecture note (1993), 2 pages.
  13. On the integration by parts formula for the SCP-integral, a project starting in 1994.
  14. Squaring the circle, a project starting in 1994 and will be a part the the possible book "Theory of Equidecomposition".
  15. On Newton-Moser iteration method and bad irrationals, an expository lecture note (1994), 7 pages.

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