Abstract
Let z be a complex variable, p a complex polynomial,and let M(p,R)=maxIp(z)I on IzI=R , M(p,1)=maxIp(z)I on IzI=1 .In this work,we investigate some new inequalities between M(p,R) and M(p^n,1)as well as between M(p^n ,R) and M(p,1) where n>2 or n=2 is a natural number.
Keywords
Mathematicle Analysis Complex Polynomials Growth of Polynomials Maximum Modulus Values Inequalities
References
- Aziz, A., (1987). Growty of Polynomials Whose Zeros are within or Outside a Circle, Bul. Austral. Math. Soc. Vol.35,
- -256.
- Aziz, A. and Dawood, M., (1988). Inequalities for a Polynomial and Its Derivative, J. Approx. Theory, 53, 155-162.
- Aziz, A. and Mohammad, O.G., (1981). Growth of Polynomials With
- Zeros Outside A Circle, Proc. Amer. Math. Soc. 81, 549-553.
- Çelik, A., (2013). Some Inequalities for Polynomial Functions, Physical Sciences (ISSN 1308-7304), Volume:8, Number:2, 32-47. DOI:10.12739/NWSA.2013.8.2.3A0064.
- Desphande, J.V., (1986). Complex Analysis (Tata McGraw- Hill
- Publishing Company, New Delhi.
- Rassias, M.Th., (1986). A New Inequality for Complex-Valued Polynomial Functions, Proc. Amer. Math. Soc. 9, 296-298
- Ankeny, N.C. and Rivlin, T.J., (1955). “On Theorem of S. Bernstein”, Pacific J. Math. 5, 849-852.
- Jain, V.K., (1998), Certain Interesting Implications of T.J. Rivlin’s Result On Maximum Modulus of A Polynomial, Glasnic
- Matematicki, Vol. 33, 33-36.
- Jain, V.K., (1999). On Polynomials Having Zeros In Closed
- Exterior or Closed Interior of a Circle, Indian J. Pure and
- Appl. Math., 153-159.
Abstract
zbir kompleks değişken,pbir kompleks polinom ve n2bir doğal
References
- Aziz, A., (1987). Growty of Polynomials Whose Zeros are within or Outside a Circle, Bul. Austral. Math. Soc. Vol.35,
- -256.
- Aziz, A. and Dawood, M., (1988). Inequalities for a Polynomial and Its Derivative, J. Approx. Theory, 53, 155-162.
- Aziz, A. and Mohammad, O.G., (1981). Growth of Polynomials With
- Zeros Outside A Circle, Proc. Amer. Math. Soc. 81, 549-553.
- Çelik, A., (2013). Some Inequalities for Polynomial Functions, Physical Sciences (ISSN 1308-7304), Volume:8, Number:2, 32-47. DOI:10.12739/NWSA.2013.8.2.3A0064.
- Desphande, J.V., (1986). Complex Analysis (Tata McGraw- Hill
- Publishing Company, New Delhi.
- Rassias, M.Th., (1986). A New Inequality for Complex-Valued Polynomial Functions, Proc. Amer. Math. Soc. 9, 296-298
- Ankeny, N.C. and Rivlin, T.J., (1955). “On Theorem of S. Bernstein”, Pacific J. Math. 5, 849-852.
- Jain, V.K., (1998), Certain Interesting Implications of T.J. Rivlin’s Result On Maximum Modulus of A Polynomial, Glasnic
- Matematicki, Vol. 33, 33-36.
- Jain, V.K., (1999). On Polynomials Having Zeros In Closed
- Exterior or Closed Interior of a Circle, Indian J. Pure and
- Appl. Math., 153-159.
Details
| Primary Language | English |
|---|---|
| Journal Section | Mathematics |
| Authors | |
| Publication Date | April 11, 2016 |
| Published in Issue | Year 2016 Volume: 11 Issue: 2 |