Study of Two Dimensional α-Modified Bernstein Bi-variate Operators

Abstract

This research work is the study of two dimensional α-Modified
Bernstein sequence of operators. Further, to investigate various approximation
results in the space of two dimensional continuous functions in terms of
these sequence of operators. Next, we estimate some lemmas in terms of test
functions and central moments. In subsequent sections, uniform convergence
and order of approximation are studied. Moreover, we prove local approximation
results in view of Lipschitz maximal functions. In the last section,
approximation results in B¨ogel-spaces are discussed with the help of mixedmodulus
of continuity.