Phillips-Type q -Bernstein Operators on Triangles

The purpose of the paper is to introduce a new analogue of Phillips-type Bernstein operators B m , q u f u , v and B n , q v f u , v , their products P m n , q f u , v and Q n m , q f u , v , their Boolean sums S m n , q f u , v and T n m , q f u , v on triangle T h , which interpolate a given function on the edges, respectively, at the vertices of triangle using quantum analogue. Based on Peano’s theorem and using modulus of continuity, the remainders of the approximation formula of corresponding operators are evaluated. Graphical representations are added to demonstrate consistency to theoretical findings. It has been shown that parameter q provides flexibility for approximation and reduces to its classical case for q = 1 .

PEANO'S THEOREM AND ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS

In this paper, we prove the existence of solutions for first order lattice dynamical systems with continuous nonlinear term obtained via discretization of a reaction–diffusion system. Since the uniqueness of the Cauchy problem is not guaranteed, we define a multivalued semiflow and prove the existence of a global compact attractor.