q-Bernstein-Schurer-Kantorovich type operators

Generalized Szász-Kantorovich Type Operators

“…In 2014, Aral et al [7] defined a generalization of Szász-Mirakyan operators and gave the quantitative type theorems in order to obtain the degree of weighted convergence by using the weighted modulus of continuity. Agrwal et al [4] presented a Stancu type Kantorovich modification of q-Bernstein-Schurer operators and established a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Atakut and Büyükyazici [8] introduced Kantorovich-Szász type operators involving Brenke polynomials and studied convergence properties of these operators by using Bohman-Korovkin's theorem.…”

Blending type approximation by generalized Bernstein-Durrmeyer type operators

“…Due to their useful structure, Bernstein polynomials and their modifications have been intensively studied. Among other papers, we refer the readers to [3,7,9,13,23,25]. For f 2 C OE0; 1; Chen et al in [10] introduced a generalization of the Bernstein operators based on a non-negative parameter˛.0 Ä˛Ä 1/ as follows: and n 2: They proved the rate of convergence, Voronovskaja type asymptotic formula and shape preserving properties for these operators.…”

Approximation by ( p , q ) $(p,q)$ -Lupaş–Schurer–Kantorovich operators

“…The development q -calculus applications established a precedent in the field of approximation theory. We may refer to some of them as Durrmeyer variant of q -Bernstein–Schurer operators [ 2 ], q -Bernstein–Schurer–Kantorovich type operators [ 3 ], q -Durrmeyer operators [ 8 ], q -Bernstein–Schurer–Durrmeyer type operators [ 12 ], q -Bernstein–Schurer operators [ 19 ], King’s type modified q -Bernstein–Kantorovich operators [ 20 ], q -Bernstein–Schurer–Kantorovich operators [ 23 ]. Lately, Mursaleen et al [ 17 ] pioneered the research of -analogue of Bernstein operators which is a generalization of q -Bernstein operators (Philips).…”