TY - JOUR
T1 - On the q-Monotonicity Preservation of Durrmeyer-Type Operators
AU - Abel, Ulrich
AU - Leviatan, Dany
AU - Raşa, Ioan
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/8
Y1 - 2021/8
N2 - We prove that various Durrmeyer-type operators preserve q-monotonicity in [0, 1] or [0 , ∞) as the case may be. Recall that a 1-monotone function is nondecreasing, a 2-monotone one is convex, and for q> 2 , a q-monotone function possesses a convex (q- 2) nd derivative in the interior of the interval. The operators are the Durrmeyer versions of Bernstein (including genuine Bernstein–Durrmeyer), Szász and Baskakov operators. As a byproduct we have a new type of characterization of continuous q-monotone functions by the behavior of the integrals of the function with respect to measures that are related to the fundamental polynomials of the operators.
AB - We prove that various Durrmeyer-type operators preserve q-monotonicity in [0, 1] or [0 , ∞) as the case may be. Recall that a 1-monotone function is nondecreasing, a 2-monotone one is convex, and for q> 2 , a q-monotone function possesses a convex (q- 2) nd derivative in the interior of the interval. The operators are the Durrmeyer versions of Bernstein (including genuine Bernstein–Durrmeyer), Szász and Baskakov operators. As a byproduct we have a new type of characterization of continuous q-monotone functions by the behavior of the integrals of the function with respect to measures that are related to the fundamental polynomials of the operators.
KW - Bernstein–Durrmeyer polynomials
KW - Szász–Durrmeyer and Baskakov–Durrmeyer operators
KW - q-monotone functions
UR - http://www.scopus.com/inward/record.url?scp=85109647128&partnerID=8YFLogxK
U2 - 10.1007/s00009-021-01823-4
DO - 10.1007/s00009-021-01823-4
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AN - SCOPUS:85109647128
SN - 1660-5446
VL - 18
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 4
M1 - 173
ER -