For investigating the approximation of Gamma operator, the characterization of approximation by Gamma operator with Jacobi weights was obtained by introducing a new ^-functional and weighted modulus of smoothness ωψ2λ(f ,t)w.
In this paper, we will introduce the weighted modulus of smoothness and the weighted K-functional to discuss the direct and the converse theorems, the local saturation results on the simultaneous approximation on an infinite interval with Jacobi-weight by the integral operator, the linear combinations of Gamma operators, for functions which is defined in the space Loo(0, 皁). The strong converse inequalities are proved for the Gamma operator.
Fourthly, the strong converse inequalities are proved for the Gamma operator that state the equivalence of two terms of error in approximation to the second modulus of smoothness with step-weight function
The rates of convergence of Post-Gamma operators for locally bounded functions is studied by means of probabilistic methods and Bojanic-cheng' s methods combining with analysis technigue, and it is proved that the estimation is asymptotically optimal for continuous points.
The study of direct and inverse theorems and equivalent theorems of some well-known linear operators (such as Bernstein, Szasz-Mirakyan, Gamma, Baskakov operator and their modification of Durrmeyer and Kantorovich) is an important research program in the theory of operator's approximation, it is also significant in theory and application.
Among the fuzzy operators, in the case in which the gamma operator (λ?=?0.975) showed the best accuracy (84.68%) while the case in which the fuzzy or operator was applied showed the worst accuracy (66.50%).
Spatial data sets such as lithology, rock weathering, geomorphology, lineaments, drainage, land use, anthropogenic factor, soil type and depth, slope gradient, and slope aspect were integrated using fuzzy gamma operator.
We give a strong converse inequality of type A in the usual sup-norm for a noncentered gamma operator Lt* , providing at the same time upper and lower constants.
The possibility measures were combined with a fuzzy gamma operator regarding the species of a certain vegetation type.