On Stancu-type integral generalization of modified Jain operators

Abstract

In this paper, we introduce a Stancu-type integral generalization of modified Lupa?-Jain operators. First, we discuss some auxiliary results and then using them we represent a Korovkin-type theorem for these operators. Next, we establish a Voronovskaja-type asymptotic result and then find a quantitative estimation for the defined operators. Also, we examine their rate of convergence with the help of modulus of continuity and the Peetre?s K-functional and analyze a convergence result for the Lipschitz-type class of functions. Lastly, we provide some graphical examples to show the relevance of our generalization.