Rahul Kumar
Department of Mathematics, School of Physical Sciences, Doon University, Dehradun, Uttarakhand, India. & Department of Mathematics, C. L. Jain College, Firozabad, Uttar Pradesh, India.

Asha Ram Gairola
Department of Mathematics, School of Physical Sciences, Doon University, Dehradun, Uttarakhand, India.

DOI https://doi.org/10.33889/IJMEMS.2026.11.2.032

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Abstract

This paper presents an approximation method of integrable functions using a modified Barbosu operator, aimed at improving the rate of convergence in function approximation on the interval [0,1]. By introducing a suitable adjustment in the weight function, we construct a sequence of positive linear operators that better preserve the function's characteristics and demonstrate superior approximation behaviour, are studied. Theoretical error bounds are established in terms of the first and second order modulus of smoothness using their equivalence with the K-functionals. Finally, numerical experiments using test functions validate the theoretical findings and confirm that the King-type modified Barbosu operator achieve better approximation performance than the usual Kantorovich type Barbosu operator.

Keywords- Linear positive operators, Rate of convergence, Modulus of smoothness, Kantorovich variant.

Citation

Kumar, R., & Gairola, A. R (2026). Approximation of Integrable Functions by Modified Barbosu Operators. International Journal of Mathematical, Engineering and Management Sciences, 11(2), 775-787. https://doi.org/10.33889/IJMEMS.2026.11.2.032.