Approximation by q-Bernstein-Stancu-Kantorovich operators with shifted knots of real parameters
M. Mursaleen, Adem Kılıçman, Md. Nasiruzzaman
Abstract
Our main purpose of this article is to study the convergence and other related properties of q-Bernstein-Kantorovich operators including the shifted knots of real positive numbers. We design the shifted knots of Bernstein-Kantorovich operators generated by the basic q-calculus. More precisely, we study the convergence properties of our new operators in the space of continuous functions and Lebesgue space. We obtain the degree of convergence with the help of modulus of continuity and integral modulus of continuity. Furthermore, we establish the quantitative estimates of Voronovskaja-type.
Topics & Concepts
MathematicsModulus of continuityConvergence (economics)Rate of convergenceType (biology)Degree (music)Mathematical analysisSpace (punctuation)Pure mathematicsAcousticsChannel (broadcasting)EcologyEconomicsEconomic growthBiologyElectrical engineeringLinguisticsPhysicsPhilosophyEngineeringApproximation Theory and Sequence SpacesMathematical Approximation and Integration