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We construct a novel family of summation-integral-type hybrid operators in terms of shape parameter  α ∈ 0,1 in this paper. Basic estimates, rate of convergence, and order of approximation are also studied using the Korovkin theorem and the modulus of smoothness. We investigate the local approximation findings for these sequences of positive linear operators utilising Peetre’s K-functional, Lipschitz class, and second-order modulus of smoothness. The approximation results are then obtained in weighted space. Finally, for these operators  q -statistical convergence is also investigated.

journal of mathematics

On Shape Parameter<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><mi>α</mi></math>-Based Approximation Properties and<math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><mi>q</mi></math>-Statistical Convergence of Baskakov-Gamma Operators

On Shape Parameterα-Based Approximation Properties andq-Statistical Convergence of Baskakov-Gamma Operators

On Shape Parameter $α$ -Based Approximation Properties and $q$ -Statistical Convergence of Baskakov-Gamma Operators