Narendra Kumar Govil

Professor
and
Undergraduate Advising Officer

Department of Mathematics & Statistics

Auburn University


photo of Dr. Govil

214-C Parker Hall (334)-844-6558

Auburn University

Auburn, AL - 36849
U.S.A.
E-mail:govilnk@auburn.edu

Teaching

Undergraduate Advising

Auburn Math Club


Lecture Notes

 

Fields: Complex Analysis, Approximation Theory

Education:

Some Selected publications:

  1. On the Summability of a Class of Fourier Series, The Mathematics Student 31 (1963), 7-12
  2. A Note on the Gibb's Phenomenon for the (^) Means of Fourier Series, Indian Journal of Mathamtics 5 (1964), 37-40.
  3. On the Summability of a Class of the Derived Conjugate Series of a Fourier Series, Canadian Mathematical Bulletin 8 (1965), 637-645.
  4. On the Strong Summability by Triangular Means of the Derived Fourier Series and its conjugate series, Canadian Mathematical Bulletin 9 (1966), 646-656.
  5. On the summability of a class of the derived Fourier series, Canadian Mathematical Bulletin 10 (1967), 79-84.
  6. On the Enestrom-Kakeya Theorem, Tohoku Mathematical Journal 20 (1968), 126-136 (with Q. I. Rahman).
  7. Functions of Exponential Type not Vanishing in a Half-Plane and Related Polynomials, Transactions of the American Mathematical Society 137 (1969), 501-517 (with Q.I. Rahman).
  8. On the Derivative of a Polynomial, Proceedings of the American Mathematical Society 41 (1973), 543-546.
  9. Inequalities for Polynomials Satisfying p(z)=z^n p(1/z), Proceedings of the American Mathematical Society 57 (1976), 238-242 (with V.K. Jain and G. Labelle).
  10. Remark on Matrix Transform of Trigonometric Series, Indain Journal of Mathematics 9 (1977), 225-229.
  11. An Inequality for Functions of Exponential Type Not Vanishing in a Half-Plane, Proceedings of the American Mathematical Society 65 (1977), 225-229.
  12. On the Enestrom-Kakeya Theorem II, Journal of Approximation Theory 22 (1978), 1-10 (with V. K. Jain).
  13. On the Location of Zeros of a Polynomial, Journal of Approximation Theory 24 (1978), 78-82, (with B. Datt).
  14. On the derivative of a polynomial, Illinois Journal of Mathematics 23 (1979), 319-329 (with Q. I. Rahman and G. Schmeisser.)
  15. On a Sequence of Fourier Coefficients, Indian Journal of Mathematics 22 (1980), 177-183 (with B.N. Sahney)
  16. An Inequality for Self-Inversive Polynomials, Journal of Mathematical Analysis and Applications 95 (1983), 490. (with K. K. Dewan).
  17. An Inequality for the Derivative of Self-Inversive Polynomials, Bulletin of the Australian Mathematical Society 27 (1983), 403-406 (with K. K. Dewan).
  18. Some Integral Inequalities for Polynomials, Indian Journal of Pure and Applied Mathematics 14 (1983), 440-443 (with K.K. Dewan).<\li>
  19. On Enestrom-Kakeya theorem, Journal of Approximation Theory 42 (1984) , 239-244 (with K. K. Dewan).
  20. On the Maximum Modulus of Polynomials, Journal of Mathematical Analysis and Applications 112 (1985), 253-258.
  21. On Bernstein's Inequality, Journal of Mathematical Analysis and Applications 126 (1987), 494-500 (with G. Labelle).
  22. On the Maximum Modulus of Polynomials not Vanishing inside the Unit Circle, Approximation Theory & its Applications 5 (1989), 79-82.
  23. Inequalities for the Derivative of a polynomial, Journal of Approximation Theory 63 (1990), 65-71.
  24. Some inequalities for Derivatives of polynomials, Journal of Approximation Theory 66 (1991), 29-35.
  25. Some Inequalities for Maximum Modulus of Polynomials, International Journal of Mathematics and Mathematical Sciences 14 (1991), 233-238.
  26. The Lie Theory for Hypergeometric Functions, Journal of Mathematical Analysis and its Applications 171 (1992), 171-204 (with H. L. Manocha).
  27. Inequalites Concerning the L^p-norm of a polynomial and its Derivative, Journal of Mathematical Analysis and Applications 179 (1993), 208-213 (with Robert B. Gardner).
  28. On Tensor Product of Finite Dimensional Irreducible Representations of sl(2,C) , International Journal of Mathematical and Statistical Sciences 2 (1993), 74-90 (with H. L. Manocha).
  29. On Polynomials with a Prescribed Zero, Journal of Mathematical Analysis and Applications 181 (1994), 282-284 (with K.K. Dewan).
  30. On the Location of the Zeros of a Polynomial, Journal of Approximation Theory 78(1994), 286-292 (with Robert B. Gardner).
  31. Some Inequalities for Entire Functions of Exponential Type, Proceedings of the American Mathematical Society 123 (1995), 2757-2761 (with Robert B. Gardner).
  32. An Lp Inequality for a Polynomial and its Derivative, Journal of Mathematical Analysis and Applications 194 (1995), 720-726 (with Robert B. Gardner).
  33. Inequalities for Polynomials Satisfying p(z)=z^n p(1/z), Complex Variables 31 (1996), 185-191 (with D.H. Vetterlein)
  34. Some Inequalities for Polynomials Satisfying p(z) = z^n p(1/z), Approximation Theory and its Applications 12 (1996), 40-44 (with Braham Datt).
  35. Some Generalizations of the Enestrom-Kakeya Theorem, Acta Mathematica Hungarica 74 (1997), 125-134 (with Robert B. Gardner).
  36. Perturbations of the Haar Wavelet, Proceedings of the American Mathematical Society 125 (1997), 3363-3370 (with R. A. Zalik).
  37. On Maximum Modulus of Polynomials Satisfying $p(z) \equiv z^np(1/z)$, East Journal on Approximations 3 (1997), 111-115. <\li>
  38. An Inequality for Self-Inversive Polynomials, Glasnik Matematicki 32 (52) (1997), 213-215. <\li>
  39. Functions of Exponential Type Not Vanishing in a Half-Plane, Analysis 17 (1997), 395-402 (with Robert B. Gardner).
  40. Bernstein Type Inequalities for Rational Functions with Prescribed Poles, Recent Progress in Inequalities (G. V. Milovanovic, Editor), 249-270, Kluwer Academic Publishers, The Netherlands (1998) (with Ram N. Mohapatra).
  41. Inequalities for Maximum Modulus of Ratioanl Functions with Prescribed Poles, Approximation Theory: In Memory of A. K. Varma (N. K. Govil, R. N. Mohapatra, Z. Nashed, A. Sharma and J. Szabados, Editors), 255-263, Marcel Dekker, Inc., New York (1998) (with R. N. Mohapatra).
  42. Markov and Bernstein Type Inequalities for Polynomials, Journal of Inequalities and Applications 3 (1999), 349-387 (with R. N. Mohapatra).
  43. On a Theorem of Ankeny and Rivlin Concerning the Maximum Modulus of Polynomials, Complex Variables 40 (2000), 249-259.
  44. L^p Inequalities for Polar Derivatives of Polynomials, Mathematical Inequalities and Applications 3 (2000) (with Griffith Nyuydinkong).
  45. Some L^p Inequalities for Polar Derivative of a Polynomial, Journal of Mathematical Analysis and Applications 254 (2001), 618-626 (with Griffith Nyuydinkong and B. Tameru).
  46. On the Maximum Modulus of Polynomials Not Vanishing inside a Circle, Journal of Interdiscilinary Mathematics 4 (2001), 93-100 (with Griffith Nyuydinkong).
  47. On Maximum Modulus of Polynomials and Related Entire Functions with Restricted Zeros, Mathematical Inequalities and Applications 5 (2002), 57-60 (with M.A. Qazi).
  48. On Growth of Polynomials, Journal of Inequalities and Applications 7 (2002), 623-631.
  49. Some Extensions of Enestrom-Kakeya Theorem, International Journal of Applied Mathematics 11 (2002), 245-253 (with G.N. McTune).
  50. L^p Inequalities for Entire Functions of Exponential Type, Mathematical Inequalities and Applications 6 (2003), 445-452.
  51. Inequalities Describing the Growth of Polynomials Not Vanishing in a Disk of Prescribed Radius, Mathematical Inequalities and Applications 6 (2003), 453-467 (with M.A. Qazi and Q.I. Rahman).
  52. A New Property of Entire Functions of Exponential Type Not Vanishing in a Half-Plane and Applications, Complex Variables 48 (2003), 897-908 (with M.A. Qazi and Q.I. Rahman).
  53. Some Generalizations Involving the Polar Derivative for an Inequality of Paul Turan, Acta Mathematica Hungarica 104 (2004), 115-126 (with G.N. McTume).
  54. Growth of Polynomials Not Vanishing Inside a Circle, International Journal of Pure and Applied Mathematics 13 (2004), 491-498 (with Robert B. Gardner and A. Weemes).
  55. Some Results Concerning Rate of Growth of Polynomial, East Journal on Approximations 10 (2004), 1-12 (with Robert B. Gardner and A. Weemes).
  56. Rate of Growth of Polynomials Not Vanishing Inside a Circle,  Journal of Inequalities in Pure and Applied Mathematics, 6 (2005),  1-9 (with Robert B. Gardner and S.N. Musukula).
  57. On the Derivative and Maximum Modulus of a Polynomial,  Journal of Inequalities and Applications 2006 (2006), 1-6 (with K. K. Dewan, A. Mir and M. S. Pukhta).
  58. Simultaneous Approximation for the Bezier Variant Baskakov Beta Operators,  Mathematical and Computer Modelling 44 (2006), 1153-1159 (with Vijay Gupta).
  59. Simultaneous Approximations for the Phillps Operators,  International Journal of Mathematics and Mathematical Sciences  2006 (2006), 1-9 (with Vijay Gupta and M.A. Noor).
  60. Rate of Convegence for Baskakov Operators on Functions of Bounded Variation,  Journal of Combinatorics, Information and System Sciences,   31 (2006), 1-17 (with Vijay Gupta).
  61. Interpolation by Polynomials and Transcendental Entire Functions, Frontiers in Interpolation and Approximation: (Dedicated to the Memory of Ambikeshwar Sharma),  173-211, Chapman & Hall/CRC Press, Taylor & Francis Group (2007) (with M. A. Qazi, and Q. I. Rahman).
  62. Some Results on Modified Sz\'asz-Mirakjan Operators, Journal of Mathematical Analysis and Applications 327 (2007), 1284-1296. (with Z. Finta and Vijay Gupta).
  63. Direct Estimates in Simultaneous Approximation for Durrmeyer Type Operators, Mathematical Inequalities and Applications 10 (2007), 371-379 (with Vijay Gupta).
  64. An inequality for entire functions of exponential type satisfying $f(z)\eqiv e^{i \gamma}e^{i\tau z}\bar{f(\bar{z})}, Acta Mathematica Hungarica 119 (2008), 189-196 (with M. A. Qazi).
  65. Convergence Rate for Generalized Baskakov Type Operators, accepted for publication in the Journal of Nonlinear Analysis, Series A: Theory, Methods & Applications (with Vijay Gupta).

Books Co-authored/ Co-Edited

  1. Fourier Analysis, Approximation Theory and their Applications, published in 1997 by New Age International (P) Limited, New Delhi, India (with Z. U. Ahmad and P. K. Jain). This book is the proceedings of the conference held at Aligarh Muslim University, India in the year 1993 on Fourier Analysis, Approximation Theory and Their Applications.
  2. Approximation Theory: - In memory of A. K. Varma, published in the year 1998 by Marcel Dekker, Inc., New York (with R. N. Mohapatra, Z. Nashed, A. Sharma and J. Szabados).
  3. Great Mathematician Srinivas Ramanujan - Life and Some Works of the Genius and Unusual Mathematician Srinivas Ramanujan, Published in Hindi, in the year 2005, by Prabhat Prakashan, New Delhi, India (with Bhu Dev Sharma).
  4. Frontiers in Interpolation and Approximation:- Dedicated to the Memory of Ambikeshwar Sharma, published in 2007 by Chapman & Hall/CRC Press, in the Series of Monographs and Textbooks, Pure and Applied Mathematics (with H.N. Mhaskar, R.N. Mohapatra, Z. Nashed, and J. Szabados).

Editing of Journals and Other Professional Activities:

  1. Editor, Journal of Inequalities in Pure and Applied Mathematics.
  2. Editor, The Australian Journal of Mathematical Analysis and Applications.
  3. Associate Editor, Journal of Inequalities and Applications.
  4. Associate Editor, European Journal of Pure and Applied Mathematics.
  5. Member of the Editorial Board of the International Journal of Mathematics and Mathematical Sciences.
  6. Member of the Editorial Board of the Journal of Mathematical Analysis and Approximation Theory.
  7. Member of the Editorial Board of the International Journal of Pure and Applied Mathematical Sciences.
  8. Member of the Editorial Board of the Global Journal of Mathematics and Mathematical Sciences.
  9. Member of the Editorial Board of Archives of Inequalities and Applications, during 2003-2004.
  10. Member of the Editorial Board of the Pan-American Mathematical Journal during 1994-98.
  11. Fellow of the National Academy of Sciences, India.
  12. Co-organized (with Professor R. A. Zalik) : Southeast Approximation Theory Conference in April 1989 at Auburn University, Auburn, Alabama.
  13. Co-organized (with Professor R.A. Zalik): A Special Session on Computational Harmomic Analysis & Approximation Theory at the 102nd Annual Meeting of the American Mathematical Society held at Orlando, Florida during January 10-13, 1996.
  14. Co-organized (with Professor Robert B. Gardner): A Special Session on Approximation Theory at the 1010th Meeting of the American Mathematical Society held at East Tennessee State University, Johnson City, during October 15-16, 2005.

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