(p, q)-Bernstein Bases and Operators over Arbitrary Intervals

摘要

In this paper, (p, q)-Bernstein bases and operators are constructed over arbitrary compact intervals. Due to the property that these bases are scale invariant but not translation invariant, the derived results on arbitrary intervals are important from computational aspects. Approximation properties of (p, q)-Bernstein operators on arbitrary compact intervals [a, b] where b a = 0 for 0 q p infinity based on Korovkin-type theorem are investigated. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical representations are added to demonstrate consistency to theoretical findings for the operators approximating functions.