Coefficient bounds for a new subclass of bi-univalent functions defined by q-fractional derivative operator

In this paper my object is, primarily, to investigate the properties of a certain operative symbol which appears to be of great utility in discussing q-functions. The first part of the paper will consist of an investigation into the various forms ofand the nature of the inverse operations symbolised by Δ−n. With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function of x.

XI.—On q -Functions and a certain Difference Operator

On the Theory of Univalent Functions

/pdf/close-to-convex-schlicht-functions-2hi8821nhv.pdf

Close-to-convex schlicht functions.

The function f(z) will be called bi-univalent if both f(z) and f-'(z) are univalent in I zI < 1; f(z) will be said to belong to oiff (i) f(z) CS and (ii) there exists a function g(z) ES such that f(g(z)) =g(f(z)) = z in some neighborhood of the origin Z Nehari remarked1 that if 4(Z) =4lz+02z2+  and i,V(z) lZ +V/2Z2 + * *, with 41, =41, are two functions mapping the open unit circle onto a schlicht domain containing the open unit circle, then the function

/pdf/on-a-coefficient-problem-for-bi-univalent-functions-1luq913hgd.pdf

Coefficient bounds for a new subclass of bi-univalent functions defined by q-fractional derivative operator

References

XI.—On q -Functions and a certain Difference Operator

On the Theory of Univalent Functions

Close-to-convex schlicht functions.

On a coefficient problem for bi-univalent functions

New subclasses of bi-univalent functions

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