KOROVKIN TYPE APROXIMATION THEOREM THROUGH STATISTICAL LACUNARY SUMMABILITY

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MURSALEEN M.; AHMAD R.

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Journal: Iranian Journal of Science Year:2013 | Volume:37 | Issue:A2 Page(s): 99-102

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Title

KOROVKIN TYPE APROXIMATION THEOREM THROUGH STATISTICAL LACUNARY SUMMABILITY

Author(s)

MURSALEEN M. | AHMAD R. | Issue Writer Certificate

Keywords

STATISTICAL CONVERGENCE

STATISTICAL LACUNARY SUMMABILITY

POSITIVE LINEAR OPERATOR

KOROVKIN TYPE APPROXIMATION THEOREM

Abstract

Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln) n³1 of POSITIVE LINEAR OPERATORs on C[0,1] of all continuous functions on the real interval [0,1] is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, x and x2 in the space C[0,1] as well as for the functions 1, cos and sin in the space of all continuous 2p-periodic functions on the real line. In this paper, we use the notion of STATISTICAL LACUNARY SUMMABILITY to improve the result of [Ann. Univ. Ferrara, 57 (2) (2011) 373-381] by using the test functions 1, e-x, e-2x n place of 1, x and x2. We apply the classical Baskakov operator to construct an example in support of our main result.

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APA: Copy

MURSALEEN, M., & AHMAD, R.. (2013). KOROVKIN TYPE APROXIMATION THEOREM THROUGH STATISTICAL LACUNARY SUMMABILITY. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 37(A2), 99-102. SID. https://sid.ir/paper/605872/en

Vancouver: Copy

MURSALEEN M., AHMAD R.. KOROVKIN TYPE APROXIMATION THEOREM THROUGH STATISTICAL LACUNARY SUMMABILITY. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE[Internet]. 2013;37(A2):99-102. Available from: https://sid.ir/paper/605872/en

IEEE: Copy

M. MURSALEEN, and R. AHMAD, “KOROVKIN TYPE APROXIMATION THEOREM THROUGH STATISTICAL LACUNARY SUMMABILITY,” IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, vol. 37, no. A2, pp. 99–102, 2013, [Online]. Available: https://sid.ir/paper/605872/en

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