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Approximation by Szász–Mirakyan–Baskakov–Stancu operators

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Abstract

This paper deals with the Stancu type generalization of Szász–Mirakyan–Baskakov operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval \([0,\infty )\). Also, Voronovskaja type theorem is studied.

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Acknowledgments

The authors would like to express their deep gratitude to the anonymous learned referee(s) and the editor for their valuable suggestions and constructive comments, which resulted in the subsequent improvement of this research article. Special thanks are due to Prof. Jacek Banasiak, Editor in chief of Afrika Matematika for kind cooperation, smooth behavior during communication and for their efforts to send the reports of the manuscript timely. The authors are also grateful to all the editorial board members and reviewers of esteemed journal i.e. Afrika Matematika. The second author PS is thankful to the Ministry of Human Resource Development, New Delhi, India for supporting this research article to carry out her research work (Ph.D. in Full-time Institute Research (FIR) category) under the supervision of Dr. Vishnu Narayan Mishra at Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat (Gujarat), India. The first author VNM acknowledges that this project was supported by the Cumulative Professional Development Allowance (CPDA), SVNIT, Surat (Gujarat), India. Both authors carried out the proof of Lemmas and Theorems. Each author contributed equally in the development of the manuscript. VNM conceived of the study and participated in its design and coordination. Both authors read and approved the final version of manuscript. The authors declare that there is no conflict of interests regarding the publication of this research article.

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Authors and Affiliations

  1. Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat, 395 007, Gujarat, India

    Vishnu Narayan Mishra & Preeti Sharma

  2. L. 1627 Awadh Puri Colony Beniganj, Phase-III, Opposite Industrial Training Institute (ITI), Ayodhya Main Road, Faizabad, 224 001, Uttar Pradesh, India

    Vishnu Narayan Mishra

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  1. Vishnu Narayan Mishra
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  2. Preeti Sharma
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Correspondence to Vishnu Narayan Mishra.

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Mishra, V.N., Sharma, P. Approximation by Szász–Mirakyan–Baskakov–Stancu operators. Afr. Mat. 26, 1313–1327 (2015). https://doi.org/10.1007/s13370-014-0288-1

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  • DOI: https://doi.org/10.1007/s13370-014-0288-1

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