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Properties of differences of meromorphic functions

Zong-Xuan Chen, Kwang Ho Shon (2011)

Czechoslovak Mathematical Journal

Let f be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference g ( z ) = f ( z + c ) - f ( z ) and the divided difference g ( z ) / f ( z ) .

Properties of functions concerned with Carathéodory functions

Mamoru Nunokawa, Emel Yavuz, Shigeyoshi Owa (2013)

Annales UMCS, Mathematica

Let Pn denote the class of analytic functions p(z) of the form p(z) = 1+cnzn + cn+1zn+1 + ... in the open unit disc U . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for p(z) concerned with Carath´eodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradović and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

Properties of harmonic conjugates

Paweł Sobolewski (2008)

Annales UMCS, Mathematica

We give a new proof of Hardy and Littlewood theorem concerning harmonic conjugates of functions u such that ∫D |u(z)|pdA(z) < ∞, 0 < p ≤ 1. We also obtain an inequality for integral means of such harmonic functions u.

Pseudo shift operators with large images

M. C. Calderón-Moreno (2002)

Colloquium Mathematicae

We give suitable conditions for the existence of many holomorphic functions f on a disc such that the image of any nonempty open subset under the action of pseudo shift operators on f is arbitrarily large. This generalizes an earlier result about images of derivatives and completes another one on infinite order differential operators.

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