Lupaş post quantum Bernstein operators over arbitrary compact intervals

  • A. Khan Aligarh Muslim University, Aligarh 202002, India
  • M. Iliyas Aligarh Muslim University, Aligarh 202002, India
  • M.S. Mansoori Aligarh Muslim University, Aligarh 202002, India
  • M. Mursaleen Aligarh Muslim University, Aligarh 202002, India; China Medical University Hospital, China Medical University, Taichung, Taiwan
Keywords: post quantum calculus, post quantum Bernstein base, post quantum Bernstein operator, modulus of continuity, convergence criteria, rate of convergence
Published online: 2021-12-28

Abstract


This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approximation properties of Lupaş post quantum Bernstein operators on arbitrary compact intervals based on Korovkin type theorem are studied. More general situation along all possible cases have been discussed favouring convergence of sequence of Lupaş post quantum Bernstein operators to any continuous function defined on compact interval. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical analysis has been presented with the help of MATLAB to demonstrate approximation of continuous functions by Lupaş post quantum Bernstein operators on different compact intervals.

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How to Cite
(1)
Khan A., Iliyas M., Mansoori M., Mursaleen M. Lupaş Post Quantum Bernstein Operators over Arbitrary Compact Intervals. Carpathian Math. Publ. 2021, 13 (3), 734-749.