In this paper we introduce a notion of F − quadratic stochastic operator. For a wide class of such operators we show that each operator of the class has unique fixed point. Also we prove that any trajectory of the F-quadratic stochastic operator converges to the fixed point exponentially fast.

A new class of harmonic multivalent functions defined by an integral operator is introduced. Coefficient inequalities, extreme points, distortion bounds, inclusion results and closure under an integral operator for this class are obtained .

This paper discusses the approximation by a Jackson-type operator on the sphere. By using a spherical translation operator, a modulus of smoothness of high order, which is used to bound the rate of approximation of the Jackson-type operator, is introduced. Furthermore, the method of multipliers is applied to characterize the saturation order and saturation class of the operator. In particular, ...

In this paper, we introduce a new class of p-valent harmonic functions defined by an integral operator. Coefficient inequalities, distortion bounds for the functions belonging to this class are obtained. The invariance of the class Hp(n, α) under convolution, convex linear combination and also under generalized Bernardi-Libera Livingston integral operator are discussed. 2000 Mathematics Subject...

A general class of linear advective PDEs, whose leading order term is of viscous dissipative type, is considered. It is proved that beyond the limit of the essential spectrum of the underlying inviscid operator, the eigenvalues of the viscous operator, in the limit of vanishing viscosity, converge precisely to those of the inviscid operator. The general class of PDEs includes the equations of i...