Baskakov operator

In functional analysis, a branch of mathematics, the Baskakov operators are generalizations of Bernstein polynomials, Szász–Mirakyan operators, and Lupas operators. They are defined by In functional analysis, a branch of mathematics, the Baskakov operators are generalizations of Bernstein polynomials, Szász–Mirakyan operators, and Lupas operators. They are defined by where x ∈ [ 0 , b ) ⊂ R {displaystyle xin [0,b)subset mathbb {R} } ( b {displaystyle b} can be ∞ {displaystyle infty } ), n ∈ N {displaystyle nin mathbb {N} } , and ( ϕ n ) n ∈ N {displaystyle (phi _{n})_{nin mathbb {N} }} is a sequence of functions defined on [ 0 , b ] {displaystyle } that have the following properties for all n , k ∈ N {displaystyle n,kin mathbb {N} } : They are named after V. A. Baskakov, who studied their convergence to bounded, continuous functions. The Baskakov operators are linear and positive.