A COEFFICIENT INEQUALITY FOR CERTAIN CLASSES OF ANALYTIC FUNCTIONS

Article Sidebar

PDF
Published: Jun 1, 1991
DOI: https://doi.org/10.5556/j.tkjm.22.1991.4588
Keywords:
Subordination convolution (Hadamard product) sub-classes of univalent analytic functions extremal functions

Main Article Content

R. M. GOEL
Department of Mathematics, Punjabi University, Patiala - 147002, Punjab (India).
BEANT SINGH MEHROK
Department of Mathematics, 17, Khalsa College, Amritsar - 143002, Punjab (India).

Abstract




Let


\[ f(z)=z+\sum_{k=2}^\infty c_kz^k \]





be analytic in the unit disc $E=\{z:|z|<1\}$. We wish to maximize $|a_3- ua_2^2|$ over certain classes of analytic functions defined by convex subordination. This paper is concerned with the solution of the above extremal problem over certain classes of univalent analytic functions.







Article Details

How to Cite
GOEL, R. M., & MEHROK, B. S. (1991). A COEFFICIENT INEQUALITY FOR CERTAIN CLASSES OF ANALYTIC FUNCTIONS. Tamkang Journal of Mathematics, 22(2), 153–163. https://doi.org/10.5556/j.tkjm.22.1991.4588
Issue
Vol. 22 No. 2 (1991)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

H. S. Al-Amiri and M.O. Reade, "On a linear combinations of some expressions in the Theory of the univalent Functions," Monatshafte fur Mathematik 80(1975), 257-264.

I. E. Bazilevic, "On the case of integrability in quadratures of the Lowner-Kufarev equation," Mat. Sb. 37(1955), 471-476.

P. N. Chichra, "New sub-classes of the class of close-to-convex functions," Proc. Amer..Math. Soc. 42(1977), 37-43.

R. M. El-Ashwah and D. K. Thomas, "Growth results for a sub-class of Bazilevic functions," Inter, J. Math. and Math. Sci. 8(1985), 785-793.

----, "Some coefficient, length area results for a sub-class of Bazilevic function" (to appear).

M. Fekete and G. Szego, "Eine Bemerkung uber ungerade Schlichte Funktionen," J. London Math. Soc. 8(1933), 85-89.

R. M. Goel and Beant Singh Mehrok, "On the coefficients of a sub--class of starlike functions," Ind. J. Pure Appl. Math. 12(1981), 634-647. ·

----, "Some invariance properties of a sub-class of close-to-convex functions," Ind. J. Pure appl. Math. 12(1981), 1240-1249.

----, "A sub-class of univalent functions," J. Aust. Math. Soc. (Series A) 35(198.3), 1-17.

J. Hummel, "The coefficient regions of starlike functions," Pacific J. Math. 7(1957), 1381-1389.

----, "Extremal problems in the class of starlike functions," Proc. Amer. Math. Soc. 11(1960), 741-749

W. Janowski, "Some extremal problems for certain families of analytic functions," Ann. Polon, Math. 28(1973), 297-326.

E. R. Keogh and E. P. Merkes, "A coefficient inequality for certain classes of analytic functions," Proc. Amer. Math. Soc. 20(1969), 8-12.

S. S. Miller, P. T. Mocanu and M. O. Reade, "All alpha-convex, functions are univalent and starlike," Proc. Amer. Math. Soc. 37(1973), 553-554.

P. T. Mocanu, "Une propriete'de convexite' generalisee clans la theorie de la representation Conforme," Mathematica (CLUJ) 11(34)(1969), 127-133.

R. Singh, "On Bazilevic functions," Proc. Amer. Math. Soc. 38(1973), 261-273.

J. Szynal, "Some Remarks on Coefficients Inequality for a-convex functions," Bull. De L'Acad. Des Sci Ser des Sci Math. Astr et phys. Vol. XX, No. 11(1972), 917-919.

D. K. Thomas, "On a sub-class of Bazilevic functions," Inter. J. Math. and Math. Sci. 8(1985), 779-783.