Sharp Coefficient Estimates Research Articles

Coefficients of multivalent symmetric functions of bounded boundary rotation

In this paper the sharp coefficient estimate problem for the classesCp(β, m) andVp(k,m) of multivalent close-to-convex functions of order β and multivalent functions of bounded boundary rotation of at mostkπ, whose functions are given bym-fold symmetric gap series, have been discussed respectively for β≥1−p/m>0 andk≥2(m/p). Moreover, it is shown that every function inVp(k,m) arep-valent close-to-convex; hencep-valent; ifk<2 (1+m/p).

A variational method for harmonic mappings onto convex regions

Harmonic mappings arise in several areas of analysis and geometry. Our purpose is to present a general variational method for treating extremal problems over families of univalent harmonic functions which map the unit disk onto a given convex region. In the special case where the target region is again the unit disk, the method leads to sharp estimates for coefficients and other functionals.

Coefficient estimates for inverses of α-spiral functions

The purpose of this note is to obtain sharp bounds for the coefficients of the inverses of univalent α-spiral functions. Further, the sharp coefficient estimates for inverses of meromorphic univalent α-spiral functions are also found.

Coefficient estimates for alpha-spiral functions

Letbelong to the class of α-spiral functions of order ρ(|α| &lt; π/2, 0 ≤ ρ &lt; 1). In this paper, we determine sharp coefficient estimates for functions of the formf(z)t, wheretis a positive integer. We also study the influence of the second coefficient on the other coefficients for such functions. The results obtained not only generalize the results of MacGregor, Boyd, Srivastava, Silverman and Silvia and others, but also give rise to new results.

Coefficient estimates for starlike functions

Let (α β) denote the class of functionsanalytic in the unit disc Δ ≡{z: |z| &lt; 1} and satisfyingfor some α, β (0 ≤ α &lt; 1, 0 &lt; β ≤ 1) and for all z ∈ Δ. In the present paper, sharp coefficient estimates for functions in (α, β) have been obtained. The results thus obtained not only generalize the corresponding results of Thomas H. MacGregor (Michigan Math. J. 10 (1963), 277–281), A.V. Boyd (Proc. Amer. Math. Soc. 17 (1966), 1016–1018) and others, but also give rise to analogous results for various other subclasses of starlike functions.

A Class of Univalent Functions

A sharp coefficient estimate is obtained for a class $D(\alpha )$ of functions univalent in the open unit disc. The radius of convexity and an arclength result are also determined for the class.

A class of univalent functions

A sharp coefficient estimate is obtained for a class D ( α ) D(\alpha ) of functions univalent in the open unit disc. The radius of convexity and an arclength result are also determined for the class.