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Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators

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Abstract

In this paper, the study of the problem of simultaneous approximation by the Szász–Mirakjan–Stancu–Durrmeyer type operators is carried out. An upper bound for the approximation to the rth-derivative of a function by these operators is established.

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Acknowledgments

The authors are extremely grateful to the anonymous learned referee(s) for their keen reading, valuable suggestion and constructive comments. The authors are very thankful to the editor(s) and their team members to consider this revised paper for reviewing again. It is this combined positiveness, which has resulted in the subsequent improvement of this research article and helped it to reach to the stage of publication. The second author RBG is thankful to Department of Mathematics, BVM Engineering College, Vallabh Vidyanagar, Anand (Gujarat) to carry out his research work (Ph.D.) under the supervision of Dr. Vishnu Narayan Mishra at Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat (Gujarat), India under PEC category. 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 paper.

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Authors and Affiliations

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

    Vishnu Narayan Mishra & R. B. Gandhi

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

    Vishnu Narayan Mishra

  3. Department of Mathematics, BVM Engineering College, Vallabh Vidyanagar, Anand, Gujarat, 388 120, India

    R. B. Gandhi

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  1. Vishnu Narayan Mishra
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Correspondence to Vishnu Narayan Mishra.

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Mishra, V.N., Gandhi, R.B. Simultaneous approximation by Szász–Mirakjan–Stancu–Durrmeyer type operators. Period Math Hung 74, 118–127 (2017). https://doi.org/10.1007/s10998-016-0145-0

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