TY  - JOUR
T1  - On the eigenstructure of the q-Stancu operator
AU  - Gürel Yılmaz, Övgü
PY  - 2024
DA  - September
Y2  - 2024
DO  - 10.31801/cfsuasmas.1388792
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 820
EP  - 832
VL  - 73
IS  - 3
LA  - en
AB  - The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, $L_{n,s,q}$, introduced by $L$. Yun and R. Wang. In this work, an explicit representation for moments of all orders has been derived. Further, it has been proved that $L_{n,s,q}$ possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived. In addition, for special choices of parameters, several eigenfunctions are depicted.
KW  - q-integers
KW  - q-Stirling
numbers
KW  - q-Stancu
operators
KW  - moments
KW  - eigenvalues
KW  - eigenfunctions
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UR  - https://doi.org/10.31801/cfsuasmas.1388792
L1  - https://dergipark.org.tr/en/download/article-file/3528795
ER  -