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BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER

Year 2014, Volume: 9 Issue: 1, 1 - 12, 01.02.2014

Adem Çelik

Abstract

D kompleks düzlemde sadece hiperbollerle sınırlı bir bölge ( bir ful hiperbolik bölge ) olsun. Bu bölgede f(0)=0, f(a)=a^q, f(-a)=-a^q olan 4m dereceli kompleks değerli ünivalent polinom fonksiyonların UT2,2^4P(a) sınıfı için maksimum modül eşitsizlikleri elde edilmiştir. Bu eşitsizliklerde katsayılar: Birincisi IaI ya bağlı olarak; bir diğeri polinomların sıfırlarına bağlı olarak, ve üçünçüsü IaI ya ve polinomların sıfırlarına bağlı olarak. Sonra bu ful hiperbolik bölgenin bir özel durumu ( Bir birim ful hiperbolik bölge) için eşitsizlikler elde edilmiştir.

Keywords

Matematik Analiz Öngörülen Üç Değeri Alan Polinom Fonksiyon Hiperbolik Bölge Maksimum Modül Değerler Eşitsizlikler

References

  • Ankeny, N.C. and Rivlin, T.J., (1955). On a theorem of S. Brenstein, Pasific J. Math., ss:849-852.
  • Aziz, A., (1987). Growty of polynomials whose zeros are within or outside a circle,Bull.Austral.Math. Soc. Vol.35, ss:247-256. Çelik, A., (2013). Inequalities for polynomial functions, NWSAPhysical Sciences, Volume: 8, Number: 2, ss:32-47.
  • DOI URL http://dx.doi.org/10.12739/NWSA.2013.8.4.3A0064
  • Çelik, A., (2012). New inequalities for Maximum Modulus Values of polynomial functions, Hacettepe Journal of Mathematics and Statistics, Volume: 41 (2), ss:255-263.
  • Çelik, A., (2009). On the ünivalent functions with three preasigned values and automorphism of an open disk, NWSAPhysical Sciences, Volume: 4, Number: 1, ss:36-41,2009.
  • Çelik, A., (2004). Maximum module values of polynomials on R z  ( ) 1  R , Üniv. Beograd, publ. Elektrotehn. Fak.,ser.Mat.15,ss:1-6 Çelik, A., (1997). A note on Mohr’s paper, Üniv.Beograd,publ. Elektrotehn. Fak., ser. Mat.8, ss: 51-54
  • Deshpande, J.V., (1986). Complex Analysis (Tata MCGraw-Hill Publising Company, New Delhi).
  • Dewan, K.K. and Ahuja, A., (2011). Growty of polynomials havings zeros inside a circle, Int. Journal of Math. Analysis, Volume:5, no.11, ss:499-505.
  • Gardner, R.B., (2004). Some results conserning rate of Growty of polynomials, East Journal on approximations, Volume: l0, Number: 3, ss:301-312.
  • Gardner, R.B., Govil, N.K., and Musukula, S.R., (2005). Rate of Growty of polynomials not vanishings inside a circle, Journal of Inequalities in Pure and Applied Mathematics, Volume: 6, Issue: 2, Articale: 53, ss:1-21.
  • Milonovic’ G.V., Mitrinovic’ D.S., and Rassias, M.TH., (1994). Extremal Problems, Inequalities Zeros (ord Scientific Publ. Co., Singapore, New Jersey, London.
  • Mir, A., Devan, K.K., and Sing, N., (2009). Some inequalities concerning the rate of growty of polinomials, Turk. J. Math., 33, ss:239-247.
  • Mohr, E., (1992). Bemerkung Zu der arbeit Van A.M. Ostrowski Notiz Uber Maximalwerte von polynomen auf dem einheitskreis Üniv. Beograd, publ. Elektrotehn. Fak,ser. Mat.3, ss: 3-4.
  • Ostrowski, A.M., (1979). Notiz uber Maximalwerte von polynomen auf dem einheitskreis, Üniv. Beograd, publ.Elektrotehn. Fak.,ser. Mat. Fiz., No 34-637 ,ss: 55-56.
  • Quazi, M.A., (1992). On the maximum module values of polynomials, Proceding of the American Mathematicle Soc., Volume: 115, Number: 2, ss:337-343.
  • Rassias, M.T.H., (1986). A new inequality for complex-valued polynomial functions, Proc. Amer. Math. Soc. 9, ss: 296-298.

INEQUALITIES IN A HIPERBOLICAL REGION

Year 2014, Volume: 9 Issue: 1, 1 - 12, 01.02.2014

Adem Çelik

Abstract

Let D (on complex plane) be a region bounded only by hyperbolas (a full hyperbolical region). In this region, we obtain the maximum modulus inequalities for the class UT2,2^4P(a) of univalent polynomial functions wth complex values of degree 4m, in which f(0)=0, f(a)=a^q, f(-a)=-a^q. The coefficients in these inequaities are obtained by three distinct ways: The firs is depending on IaI; the other one is depending on the zeros of polynomials, and the third is depending on IaI and on the zeros of polynomials. Then we obtain inequalities for the special case where our region is unit full hyperbolical region.

Keywords

Mathematical Analysis Polynomials Functions with Three Preasigned Values Hiperbolical Region Maximum Modulus Values Inequalities

References

  • Ankeny, N.C. and Rivlin, T.J., (1955). On a theorem of S. Brenstein, Pasific J. Math., ss:849-852.
  • Aziz, A., (1987). Growty of polynomials whose zeros are within or outside a circle,Bull.Austral.Math. Soc. Vol.35, ss:247-256. Çelik, A., (2013). Inequalities for polynomial functions, NWSAPhysical Sciences, Volume: 8, Number: 2, ss:32-47.
  • DOI URL http://dx.doi.org/10.12739/NWSA.2013.8.4.3A0064
  • Çelik, A., (2012). New inequalities for Maximum Modulus Values of polynomial functions, Hacettepe Journal of Mathematics and Statistics, Volume: 41 (2), ss:255-263.
  • Çelik, A., (2009). On the ünivalent functions with three preasigned values and automorphism of an open disk, NWSAPhysical Sciences, Volume: 4, Number: 1, ss:36-41,2009.
  • Çelik, A., (2004). Maximum module values of polynomials on R z  ( ) 1  R , Üniv. Beograd, publ. Elektrotehn. Fak.,ser.Mat.15,ss:1-6 Çelik, A., (1997). A note on Mohr’s paper, Üniv.Beograd,publ. Elektrotehn. Fak., ser. Mat.8, ss: 51-54
  • Deshpande, J.V., (1986). Complex Analysis (Tata MCGraw-Hill Publising Company, New Delhi).
  • Dewan, K.K. and Ahuja, A., (2011). Growty of polynomials havings zeros inside a circle, Int. Journal of Math. Analysis, Volume:5, no.11, ss:499-505.
  • Gardner, R.B., (2004). Some results conserning rate of Growty of polynomials, East Journal on approximations, Volume: l0, Number: 3, ss:301-312.
  • Gardner, R.B., Govil, N.K., and Musukula, S.R., (2005). Rate of Growty of polynomials not vanishings inside a circle, Journal of Inequalities in Pure and Applied Mathematics, Volume: 6, Issue: 2, Articale: 53, ss:1-21.
  • Milonovic’ G.V., Mitrinovic’ D.S., and Rassias, M.TH., (1994). Extremal Problems, Inequalities Zeros (ord Scientific Publ. Co., Singapore, New Jersey, London.
  • Mir, A., Devan, K.K., and Sing, N., (2009). Some inequalities concerning the rate of growty of polinomials, Turk. J. Math., 33, ss:239-247.
  • Mohr, E., (1992). Bemerkung Zu der arbeit Van A.M. Ostrowski Notiz Uber Maximalwerte von polynomen auf dem einheitskreis Üniv. Beograd, publ. Elektrotehn. Fak,ser. Mat.3, ss: 3-4.
  • Ostrowski, A.M., (1979). Notiz uber Maximalwerte von polynomen auf dem einheitskreis, Üniv. Beograd, publ.Elektrotehn. Fak.,ser. Mat. Fiz., No 34-637 ,ss: 55-56.
  • Quazi, M.A., (1992). On the maximum module values of polynomials, Proceding of the American Mathematicle Soc., Volume: 115, Number: 2, ss:337-343.
  • Rassias, M.T.H., (1986). A new inequality for complex-valued polynomial functions, Proc. Amer. Math. Soc. 9, ss: 296-298.
There are 16 citations in total.

Details

Primary Language Turkish
Journal Section Physics
Authors

Adem Çelik This is me

Publication Date February 1, 2014
Published in Issue Year 2014 Volume: 9 Issue: 1

Cite

APA Çelik, A. (2014). BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER. Physical Sciences, 9(1), 1-12. https://doi.org/10.12739/NWSA.2014.9.1.3A0065
AMA Çelik A. BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER. Physical Sciences. February 2014;9(1):1-12. doi:10.12739/NWSA.2014.9.1.3A0065
Chicago Çelik, Adem. “BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER”. Physical Sciences 9, no. 1 (February 2014): 1-12. https://doi.org/10.12739/NWSA.2014.9.1.3A0065.
EndNote Çelik A (February 1, 2014) BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER. Physical Sciences 9 1 1–12.
IEEE A. Çelik, “BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER”, Physical Sciences, vol. 9, no. 1, pp. 1–12, 2014, doi: 10.12739/NWSA.2014.9.1.3A0065.
ISNAD Çelik, Adem. “BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER”. Physical Sciences 9/1 (February 2014), 1-12. https://doi.org/10.12739/NWSA.2014.9.1.3A0065.
JAMA Çelik A. BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER. Physical Sciences. 2014;9:1–12.
MLA Çelik, Adem. “BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER”. Physical Sciences, vol. 9, no. 1, 2014, pp. 1-12, doi:10.12739/NWSA.2014.9.1.3A0065.
Vancouver Çelik A. BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER. Physical Sciences. 2014;9(1):1-12.