a b s t r a c tIn this paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients |a 2 | and |a 3 | for functions in these new subclasses.

Abstract. We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes.Mathematics subject classification (2010): Primary 30C45; Secondary 30C80.

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The main cause of death related to cancer worldwide is from hepatic cancer. Detection of hepatic cancer early using computed tomography (CT) could prevent millions of patients’ death every year. However, reading hundreds or even tens of those CT scans is an enormous burden for radiologists. Therefore, there is an immediate need is to read, detect, and evaluate CT scans automatically, quickly, and accurately. However, liver segmentation and extraction from the CT scans is a bottleneck for any system, and is still a challenging problem. In this work, a deep learning-based technique that was proposed for semantic pixel-wise classification of road scenes is adopted and modified to fit liver CT segmentation and classification. The architecture of the deep convolutional encoder–decoder is named SegNet, and consists of a hierarchical correspondence of encode–decoder layers. The proposed architecture was tested on a standard dataset for liver CT scans and achieved tumor accuracy of up to 99.9% in the training phase.

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Abstract. The main object of this paper is to study the class T¿ iC (a, β) of analytic functions with negative coefficients and with fixed second coefficients. Among other results of interest, we derive coefficient estimates, closure properties involving convex linear combinations, growth and distortion theorems, and radii of starlikeness and convexity for functions in the class T* c (q, β). Many of these results are further extended to hold true for families of functions with finitely many fixed coefficients.

We investigate convolution properties and coefficients estimates for two classes of analytic functions involving the -derivative operator defined in the open unit disc. Some of our results improve previously known results.

Radius of starlikeness of order α Radius of convexity of order α a b s t r a c t Let S * (q c ), c ∈ (0, 1], denote the class of analytic functions f in the unit disc U normalized by f (0) = f ′ (0) − 1 = 0 and satisfying the conditionThe relations between S * (q c ) and other classes geometrically defined are considered. The radii of convexity (starlikeness) of order α are calculated. The same problem in the class of strongly starlike functions of order β is also considered.