Iterates of q-Bernstein operators on triangular domain with all curved sides

Abstract

In this article, Phillips-type Bernstein operators (ℬm,qtF)(t,s)({{\mathcal{ {\mathcal B} }}}_{m,q}^{t}F)\left(t,s) and (ℬn,qsF)(t,s)({{\mathcal{ {\mathcal B} }}}_{n,q}^{s}F)\left(t,s), their products, and Boolean sum based on q-integer have been studied on a triangle with all curved sides. Furthermore, convergence of iterates of these operators have been analyzed using the weakly Picard operators technique and the contraction principle.

Keywords

• quantum calculus
• phillips q-bernstein operators
• product operators
• boolean sum operators
• weakly picard operators
• contraction principle
• 41a05
• 41a35
• 41a36