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On Integral Means for Fractional Calculus Operators of Multivalent Functions

Sümer Eker, S., Özlem Güney, H., Owa, Shigeyoshi (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80Integral means inequalities are obtained for the fractional derivatives and the fractional integrals of multivalent functions. Relevant connections with various known integral means inequalities are also pointed out.

On local injectivity and asymptotic linearity of quasiregular mappings

V. Gutlyanskiĭ, O. Martio, V. Ryazanov, M. Vuorinen (1998)

Studia Mathematica

It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at x 0 implies the local injectivity and the asymptotic linearity of f at x 0 . Sufficient conditions for l o g | f ( x ) - f ( x 0 ) | to behave asymptotically as l o g | x - x 0 | are given. Some global injectivity results are derived.

On locally biholomorphic mappings from multi-connected onto simply connected domains

Piotr Liczberski, Victor V. Starkov (2005)

Annales Polonici Mathematici

We continue E. Ligocka's investigations concerning the existence of m-valent locally biholomorphic mappings from multi-connected onto simply connected domains. We decrease the constant m, and also give the minimum of m in the case of mappings from a wide class of domains onto the complex plane ℂ.

On locally biholomorphic surjective mappings

Ewa Ligocka (2003)

Annales Polonici Mathematici

We prove that each open Riemann surface can be locally biholomorphically (locally univalently) mapped onto the whole complex plane. We also study finite-to-one locally biholomorphic mappings onto the unit disc. Finally, we investigate surjective biholomorphic mappings from Cartesian products of domains.

On maximum modulus for the derivative of a polynomial

K. Dewan, Sunil Hans (2009)

Annales UMCS, Mathematica

If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

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