


Paper's Title:
Fractional class of analytic functions Defined Using qDifferential Operator
Author(s):
K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan
Department of Mathematics and
Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
Email: kr_karthikeyan1979@yahoo.com
College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
Email: musthafa.ibrahim@gmail.com
Department of Mathematics, Presidency
College (Autonomous),
Chennai600005, Tamilnadu,
India.
Abstract:
We define a qdifferential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving qdifferential fractional operator. We also determine the necessary and sufficient conditions for functions to be in the class. Further, we obtain the coefficient estimates, extreme points, growth and distortion bounds.
Paper's Title:
Some properties of quasinormal, paranormal and 2k^{*} paranormal operators
Author(s):
Shqipe Lohaj
Department of Mathematics,
University of Prishtina,
10000,
Kosova.
Email: shqipe.lohaj@unipr.edu
Abstract:
In the beginning of this paper some conditions under which an operator is partial isometry are given. Further, the class of 2k^{*} paranormal operators is defined and some properties of this class in Hilbert space are shown. It has been proved that an unitarily operator equivalent with an operator of a 2k^{*} paranormal operator is a 2k^{*} paranormal operator, and if is a 2k^{*} paranormal operator, that commutes with an isometric operator, then their product also is a $2k^*$ paranormal operator.
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