Approximation properties by summation integral type operators

In this thesis, we investigated the approximation properties of a general familyof summation integral type linear positive operators Gn ,c , defined by Srivastavaand Gupta, in different function spaces. Firstly, we investigated the weightedapproximation properties of the sequence of the operators Gn ,c for continuousfunctions on [0, ∞) and having polynomial growth at infinity. We estimated rateof convergence of these operators in terms of the weighted modulus ofcontinuity. Secondly, we studied the properties of simultaneous approximationby the operators Gn,c . We established the basic pointwise convergence theoremand Voronowskaja type asymptotic approximation theorem. Moreover, we gavean estimate of degree of approximation by Gn ,c for smooth functions. Finally, weintroduced the Bezier variant of the operators Gn ,c and obtained an estimate ofthe rate of convergence of sequence of these operators for functions of boundedvariation.Science Code : 204.1.095Key Words : Summation integral type operators, rate of convergence,simultaneous convergence, Bezier variant, boundedvariation functions.