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In this paper, we investigate a variant of the Jain operators, which preserve the linear functions. We compute the rate of convergence of these operators with the help of K-functional. We also introduce modifications of the Jain operators based on the models in [4] and [10]. These modified operators yield better error estimates than the Jain operators.

In the present paper, a bivariate generalization of the q-Szász-Mirakjan-Kantorovich operators is constructed by q R -integral and these operators' weighted A-statistical approximation properties are established. Also, we estimate the rate of pointwise convergence of the proposed operators by modulus of continuity. MSC: 41A25; 41A36

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