Modified Post-Widder Operators Preserving Exponential Functions

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


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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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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