The symmetric difference is a robust operator for measuring the error of approximating one shape by another. Given two convex shapes P and C, we study the problem of minimizing the volume of their symmetric difference under all possible scalings and translations of C. We prove that the problem can be solved by convex programming. We also present a combinatorial algorithm for convex polygons in ...

In this paper we introduce new subclasses of k-uniformly convex and starlike functions with respect to other points. We provide necessary and sufficient conditions, coefficient estimates, distortion bounds, extreme points and radii of close-to-convexity, starlikeness and convexity for these classes. We also obtain integral means inequalities with the extremal functions for these classes.

In the present paper, we obtain coefficient estimates for new subclass of analytic functions with respect to symmetric points. A sufficient condition for a function to belong to this class of function is also obtained.

In the present paper, we introduce two new subclasses B (k) λ (α) and L (k) λ (α) of analytic functions with respect to k-symmetric points. Some coefficient inequalities for functions belonging to these classes and their subclasses with positive coefficients are provided.

A continuous function f = u + iv is a complex valued harmonic function in a complex domain C if both u and v are real harmonic in C. In any simply connected domain D ⊂ C we can write f(z) = h + g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and sense-preserving in D is that |h′(...

In the present paper, we introduce two new subclasses P sc (λ, α) and Q sc (λ, α) of analytic functions with respect to 2k-symmetric conjugate points. Such results as integral representations, convolution conditions and coefficient inequalities for these classes are provided. 2000 Mathematics Subject Classification. Primary 30C45.

The criteria that embed a normalized analytic function in the class of functions that are starlike with respect to N-symmetric points are presented. The criteria are based on the quotient of analytical representations of starlikeness and convexity with respect to N -symmetric points. AMS Mathematics Subject Classification (2000): 30C45