On Stancu operators depending on a non-negative integer
Tuğba Bostancı, Gülen Başcanbaz‐Tunca
Abstract
In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, we define Kantorovich extension of the operators. For functions belonging to the space Lp [0, 1] , 1 ? p < ?, we obtain convergence in the norm of Lp by the sequence of Stancu-Kantorovich operators, and we give an estimate for the rate of the convergence via first order averaged modulus of smoothness. Moreover, for the Stancu operators; we search variation detracting property and convergence in the space of functions of bounded variation in the variation seminorm.
Topics & Concepts
MathematicsRate of convergenceNorm (philosophy)Bounded functionInteger (computer science)Bounded variationOperator normSequence (biology)Convergence (economics)Variation (astronomy)Order (exchange)Discrete mathematicsMathematical analysisEconomicsGeneticsBiologyPhysicsPolitical scienceLawProgramming languageElectrical engineeringComputer scienceEngineeringAstrophysicsEconomic growthFinanceChannel (broadcasting)Approximation Theory and Sequence SpacesMathematical Approximation and IntegrationAdvanced Harmonic Analysis Research