Korovkin type theorem in the space C̃ b [ 0 , ∞ )
نویسنده
چکیده
A Korovkin type theorem is established in the space C̃b[0,∞) of all uniformly continuous and bounded functions on [0,∞) for a sequence of positive linear operators, the approximation error being estimated with the aid of the usual modulus of continuity. As applications we obtain quantitative results for q-Baskakov operators. Mathematics Subject Classification (2010): 41A36, 41A25.
منابع مشابه
Approximation for periodic functions via weighted statistical convergence
Keywords: Density Statistical convergence Weighted statistical convergence Positive linear operator Korovkin type approximation theorem a b s t r a c t Korovkin type approximation theorems are useful tools to check whether a given sequence ðL n Þ nP1 of positive linear operators on C½0; 1 of all continuous functions on the real interval ½0; 1 is an approximation process. That is, these theore...
متن کاملA-statistical Korovkin-type Approximation Theorem for Functions of Two Variables on an Infinite Interval
In this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0,∞) × [0,∞) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical v...
متن کاملMatrix Summability and Korovkin Type Approximation Theorem on Modular Spaces
In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.
متن کاملKorovkin Second Theorem via B-Statistical A-Summability
and Applied Analysis 3 f continuous on R. We know that C(R) is a Banach space with norm f ∞ := sup x∈R f (x) , f ∈ C (R) . (12) We denote by C 2π (R) the space of all 2π-periodic functions f ∈ C(R) which is a Banach space with f 2π = sup t∈R f (t) . (13) The classical Korovkin first and second theorems statewhatfollows [15, 16]: Theorem I. Let (T n ) be a sequence of p...
متن کاملKorovkin type approximation theorem for functions of two variables in statistical sense
In this paper, using the concept of A -statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical versi...
متن کامل