On an approximation process of integral type

Some approximation properties of a new class of linear operators

“…In the particular case a = e, the operators defined in Equation (14) convert to Jain operator 9 ; = 0, a = e, the operators P [ , a] n , n ∈ N, turn into well-known Szàsz-Mirakjan operators. 2 This operators have different approximation properties than the operators discussed by Szász 2 and Jain.…”

“…The relation between the local smoothness of function and local approximation, the degree of approximation, and the statistical convergence of the Jain operators were studied by Agratini . The Durrmeyer‐type generalizations of the Jain operators and its approximation properties were elaborated by Tarabie, Mishra and Patel, and Agratini . The generalized Jain operators as variant of the Lupaş operators were studied by Patel and Mishra .…”

A Study on the Rate of Convergence of Chlodovsky-Durrmeyer Operator and Their Bézier Variant

“…Several researchers have studied approximation properties of the operators M n ( [8], [10]) for function of bounded variation defined on the interval [0,1]. After that Zeng and Chen [22] …”

“…Recently Agratini [1], Aniol and Pych-Taberska [3], Pych-Taberska [20], and Gupta [11,12] have investigated the rate of pointwise convergence for Kantorovich and Durrmeyer Type Baskakov-Bézier and Bézier operators using a different approach. They have proved their theorems in terms of the Chanturia modulus of variation, which is a generalization of the classical Jordan variation.…”

On new class of linear and positive operators

“…Due to intersecting properties of the Szász-Mirakyan operators, these operators have been intensively studied by many mathematicians [8][9][10][11][12]. Furthermore, its modification the Jain operators and its different generalizations were also discussed by many researchers in recent years, see [13][14][15][16][17][18]. This motivated us to generalize Jain operators as variant of the Lupaş operators defined by (1.1).…”