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Local approximation properties for certain King type operators

Ozarslan Ali Mehmet (Department of Mathematics, Eastern Mediterranean University,Gazimagusa, TRNC, Mersin, Turkey)
Aktuglu Hüseyin (Department of Mathematics, Eastern Mediterranean University,Gazimagusa, TRNC, Mersin, Turkey)

In this paper, we consider a certain King type operators which includes general families of Szász-Mirakjan, Baskakov, Post-Widder and Stancu operators. By introducing two parameter family of Lipschitz type space, which provides global approximation for the above mentioned operators, we obtain the rate of convergence of this class. Furthermore, we give local approximation results by using the first and the second modulus of continuity.

Keywords: Positive linear operators, Lipschitz type space, Szász-Mirakjan operators, Baskakov operators, Post-Widder operators, Stancu operators, modulus of continuity