A Sequence of Kantorovich-Type Operators on Mobile Intervals

Authors : Mirella CAPPELLETTI MONTANO, Vita LEONESSA

Pages : 130-143

Doi:10.33205/cma.571078

View : 12 | Download : 6

Publication Date : 2019-09-01

Article Type : Research Paper

Abstract :In this paper, we introduce and study a new sequence of positive linear operators, acting on both spaces of continuous functions as well as spaces of integrable functions on $[0, 1]$. We state some qualitative properties of this sequence and we prove that it is an approximation process both in $Cinsert ignore into journalissuearticles values([0, 1]);$ and in $L^pinsert ignore into journalissuearticles values([0, 1]);$, also providing  some estimates of the rate of convergence. Moreover, we determine an asymptotic formula and, as an application,  we  prove that certain iterates of the operators converge, both in $Cinsert ignore into journalissuearticles values([0, 1]);$ and, in some cases,  in $L^pinsert ignore into journalissuearticles values([0, 1]);$, to a limit semigroup. Finally, we show that our operators, under suitable hypotheses, perform better than  other existing ones in the literature. 
Keywords : Kantorovich type operators, Positive approximation processes, Rate of convergence, Asymptotic formula, Generalized convexity