On approximation and interpolation errors of analytic functions

• Autorzy: Kumar D.
• Języki publikacji: EN

Abstrakty

EN

Kasana and Kumar [5] obtained the (p. q)—growth parameters in terms of Chebyshev and interpolation errors for entire functions on a compact set E of positive transfinite diameter. Rizvi and Nautiyal [9] studied the order and type in terms of these errors for the functions which are not entire. But these results do not give any specific information about the growth of non-entire functions if maximum modules is increasing so rapidly that the order of function is infinite. In this paper an attempt has been made to extend the results contained in [9] for functions having rapidly increasing maximum modulus.

Słowa kluczowe

EN

largest equipotential curve; regularity domain; approximation error; interpolation error

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2007
• Tom: Nr 38
• Strony: 47--56
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kumar D.

• Department of Mathemactics, D.S.M. Degree College, Kanth-244 501 (Moradabad), U.P., India,

Bibliografia

• [1] BAJPAI S.K., KAPOOR G.P., JUNEJA O.P., On entire functions of fast growth, Trans. Amer. Math. Soc., 203(1975), 275-298.
• [2] BERNSTEIN S.N., Lecons sur les properties extremales et al meilleure approximation des functions analytiques d'une variable seele, Gauthier- Villars, Paris 1926.
• [3] JUNEJA O.P., Approximation of an entire function, J. Approx. Theory, 11 (1974), 343-349.
• [4] KAPOOR G.P., GOPAL K., On the coefficients of functions analytic in the unit disc having fast rates of growth, Annali di Matematica Pura ed Applicata, 61 (1979), 331-349.
• [5] KASANA H.S., KUMAR D., On approximation and interpolation of entire function with index-pair (p,q), Publications Matematiques, 38(1994), 255-267.
• [6] REDDY A.R., Approximation of an entire function, J. Approx. Theory, 3(1970), 128-137.
• [7] REDDY A.R., Best polynomial approximation to certain entire functions, J. Approx. Theory, 5 (1972), 97-112.
• [8] RICE J.R., The degree of convergence for entire functions, Duke Math. J., 38(1971), 429-440.
• [9] RIZVI S.R.H., NAUTIYAL A., On the approximation and interpolation of an analytic function, Math. Student, 49(3)(1981), 281-290.
• [10] SHAH S.M., Polynomial approximation of an entire function and generalized orders, J. Approx. Theory, 19(1977), 315-324.
• [11] SlCIAK J., On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc., 105(1962), 322-357.
• [12] SlCIAK J., Approximation by transcendental polynomials, Ann. Polon. Math., 46(1985), 299-309.
• [13] SMIRNOV V.I., LEVEDEV N.A., Functions of a Complex Variable: Constructive Theory, M.I.T. Press, Mass., U.S.A. 1968. [14] VARGA R.S., On an extension of a result of S.N. Bernstein, J. Approx. Theory, 1(1968), 176-179.
• [15] WALSH J.L., Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Providence, R.I. 1935.
• [16] WINIARSKI T.N., Approximation and interpolation of entire functions, Ann. Polon. Math., 23(1970), 259-273.