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Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We introduce the notions of weighted lacunary statistical pointwise and uniform convergence and a kind of convergence which is lying between aforementioned convergence methods, namely, weighted lacunary equi-statistical convergence and obtain various implication results with supporting examples. We then apply our new concept of weighted lacunary equi-statistical convergence with a view to proving Korovkin and Voronovskaya type approximation theorems. We also construct an example with the help of generating functions type Meyer-König and Zeller which shows that our Korovkin-type theorem is stronger than its classical version. Moreover, we compute the rate of weighted lacunary equi-statistical convergence for operators in terms of modulus of continuity.

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Acknowledgements

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant no. (G-296-130-38). The authors, therefore, acknowledge with thanks DSR for technical and financial support.

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Authors and Affiliations

  1. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine & Badriah A. S. Alamri

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  1. S. A. Mohiuddine
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  2. Badriah A. S. Alamri
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Correspondence to S. A. Mohiuddine.

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Mohiuddine, S.A., Alamri, B.A.S. Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems. RACSAM 113, 1955–1973 (2019). https://doi.org/10.1007/s13398-018-0591-z

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  • DOI: https://doi.org/10.1007/s13398-018-0591-z

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