Turan, Mehmet

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https://hdl.handle.net/20.500.14411/6771
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T., Mehmet
Turan M.
M.,Turan
Turan,Mehmet
Mehmet, Turan
T.,Mehmet
Turan A.
Mehmet Turan
M., Turan
Turan, Mehmet
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Turan, M.
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mehmet.turan@atilim.edu.tr
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Mathematics
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Scholarly Output

55

Articles

44

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25/0

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5

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2

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83

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96

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1.51

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1.75

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13

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7

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Mathematica Slovaca3
Mathematical Methods in the Applied Sciences3
Quaestiones Mathematicae2
Results in Mathematics2
Bulletin of the Malaysian Mathematical Sciences Society2
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Author: Turan, MehmetSubject: q-Durrmeyer operator

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Now showing 1 - 4 of 4
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    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Rate of Convergence for the q-durrmeyer Polynomials in Complex Domains
    (Walter de Gruyter Gmbh, 2024) Gurel, Ovgu; Ostrovska, Sofiya; Turan, Mehmet
    The q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set D subset of C, the rate of convergence is O(q(n)) as n -> infinity. The sharpness of the obtained result is demonstrated.
  • Thumbnail Image
    Article
    Citation - WoS: 2
    Citation - Scopus: 2
    The Impact of the Limit q-durrmeyer Operator on Continuous Functions
    (Springer Heidelberg, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet; Gurel Yilmaz, Ovgu
    The limit q-Durrmeyer operator, D-infinity,D-q, was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172-178, 2008) during a study of q-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of D-infinity,D-q. The interrelation between the analytic properties of a function f and the rate of growth for D(infinity,q)f are established, and the sharpness of the obtained results are demonstrated.
  • Thumbnail Image
    Article
    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; Gürel Yılmaz, Övgü
    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.
  • Thumbnail Image
    Article
    On the Continuity in q of the Family of the Limit q-durrmeyer Operators
    (de Gruyter Poland Sp Z O O, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet; Gurel Yilmaz, Ovgu; Yllmaz, Övgü Gürel
    This study deals with the one-parameter family {D-q}(q is an element of[0,1]) of Bernstein-type operators introduced by Gupta and called the limit q-Durrmeyer operators. The continuity of this family with respect to the parameter q is examined in two most important topologies of the operator theory, namely, the strong and uniform operator topologies. It is proved that {D-q}(q is an element of[0,1]) is continuous in the strong operator topology for all q is an element of [0, 1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 and fails at all q is an element of (0, 1]. In addition, a few estimates for the distance between two limit q-Durrmeyer operators have been derived in the operator norm on C[0, 1].