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Modified Post-Widder Operators Preserving Exponential Functions

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Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 41)

Abstract

The paper considers a modification \(\widetilde {P}_n\) of the Post-Widder operators, which contains two auxiliary functions an(x), bn(x). The main result consists of the conclusion that under an appropriate choice of an(x), bn(x), the operator \(\widetilde {P}_n: C[0,\infty )\to C[0,\infty )\) has two eigenfunctions exp(cix) associated with the same unit eigenvalue. Here, c1 < c2 are real numbers. We establish direct estimates, including a quantitative asymptotic formula for the modified form of the operators. Finally, we represent the error graphically using the software Mathematica.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsNetaji Subhas University of Technology (Formerly Netaji Subhas Institute of Technology)New DelhiIndia
  2. 2.Department of Applied Science and HumanitiesInderprastha Engineering CollegeGhaziabadIndia

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