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Citation - WoS: 1
Citation - Scopus: 1
Shape-Preserving Properties of the Limit q-durrmeyer Operator
(Academic Press inc Elsevier Science, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet
The present work aims to establish the shape-preserving properties of the limit q- Durrmeyer operator, D q for 0 < q < 1. It has been proved that the operator is monotonicity- and convexity-preserving. What is more, it maps a function m - convex along {q (j)}(infinity)(j =0) to a function m - convex along any sequence { xq( j )}(infinity)(j =0) , x is an element of (0, 1). (c) 2024 Elsevier Inc. All rights reserved.
On the Image of the Lupas q-analogue of the Bernstein Operators
(Springernature, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet
The Lupas q-analogue, R-n,R-q, is historically the first known q-version of the Bernstein operator. It has been studied extensively in different aspects by a number of authors during the last decades. In this work, the following issues related to the image of the Lupas q-analogue are discussed: A new explicit formula for the moments has been derived, independence of the image R-n,R-q from the parameter q has been examined, the diagonalizability of operator R-n,R-q has been proved, and the fact that R-n,R-q does not preserve modulus of continuity has been established.