A comprehensive study on the shape properties of Kantorovich type Schurer operators equipped with shape parameter λ
This study explores the shape-preserving characteristics of the Kantorovich variant of λ−Schurer operators which are a modified version of the classical Kantorovich-type Schurer operators enhanced by the introduction of a shape parameter λ∈−1,1. The underlying objective of this study is to analyze h...
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| Veröffentlicht in: | Expert systems with applications Jg. 270; S. 126500 |
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| Sprache: | Englisch |
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25.04.2025
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| Abstract | This study explores the shape-preserving characteristics of the Kantorovich variant of λ−Schurer operators which are a modified version of the classical Kantorovich-type Schurer operators enhanced by the introduction of a shape parameter λ∈−1,1. The underlying objective of this study is to analyze how these operators retain the intrinsic geometric characteristics of the functions they approximate, a quality essential in applications such as computer graphics, signal processing, geometric modeling, robotics, and so forth. To accomplish this task, we begin by representing the operators in question as a sum of the classical Kantorovich-type Schurer operators and an additional term involving the integral of first-order divided differences of the function ℓ, where this additional term is scaled by the shape parameter λ. Using this formulation and the fundamental properties of divided differences, we then investigate the shape-preserving characteristics of these operators, including linearity, positivity, and, in particular, their ability to maintain monotonicity and convexity in relation to the function ℓ. The outcomes of this study show that the operators fully preserve monotonicity over the interval 0,1 for all λ∈−1,1, but fail to consistently preserve convexity for certain values of λ within the same range. We support this conclusion with counterexamples and provide an adjusted result on convexity preservation for a particular class of functions when λ is chosen from the interval 0,1. We conclude our analysis with a section focusing on the convexity-preserving comparison of operators characterized by the shape parameter λ.
•Integration of shape parameter λ into Kantorovich type Schurer operators for enhanced adaptability.•Operators preserve monotonicity across all λ values and partially preserve convexity.•Relevant for geometric modeling, computer graphics, and signal processing. |
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| AbstractList | This study explores the shape-preserving characteristics of the Kantorovich variant of λ−Schurer operators which are a modified version of the classical Kantorovich-type Schurer operators enhanced by the introduction of a shape parameter λ∈−1,1. The underlying objective of this study is to analyze how these operators retain the intrinsic geometric characteristics of the functions they approximate, a quality essential in applications such as computer graphics, signal processing, geometric modeling, robotics, and so forth. To accomplish this task, we begin by representing the operators in question as a sum of the classical Kantorovich-type Schurer operators and an additional term involving the integral of first-order divided differences of the function ℓ, where this additional term is scaled by the shape parameter λ. Using this formulation and the fundamental properties of divided differences, we then investigate the shape-preserving characteristics of these operators, including linearity, positivity, and, in particular, their ability to maintain monotonicity and convexity in relation to the function ℓ. The outcomes of this study show that the operators fully preserve monotonicity over the interval 0,1 for all λ∈−1,1, but fail to consistently preserve convexity for certain values of λ within the same range. We support this conclusion with counterexamples and provide an adjusted result on convexity preservation for a particular class of functions when λ is chosen from the interval 0,1. We conclude our analysis with a section focusing on the convexity-preserving comparison of operators characterized by the shape parameter λ.
•Integration of shape parameter λ into Kantorovich type Schurer operators for enhanced adaptability.•Operators preserve monotonicity across all λ values and partially preserve convexity.•Relevant for geometric modeling, computer graphics, and signal processing. |
| ArticleNumber | 126500 |
| Author | Ödemiş Özger, Zeynep Özger, Faruk Turhan, Nezihe |
| Author_xml | – sequence: 1 givenname: Nezihe orcidid: 0000-0002-9012-4386 surname: Turhan fullname: Turhan, Nezihe email: nezihe.turhan.turan@ikcu.edu.tr organization: Department of Engineering Sciences, Izmir Katip Celebi University, 35620 Izmir, Turkey – sequence: 2 givenname: Faruk orcidid: 0000-0002-4135-2091 surname: Özger fullname: Özger, Faruk email: farukozger@gmail.com organization: Department of Computer Engineering, Iğdır University, 76000, Iğdır, Turkey – sequence: 3 givenname: Zeynep orcidid: 0000-0002-3941-1726 surname: Ödemiş Özger fullname: Ödemiş Özger, Zeynep email: zeynep.odemis.ozger@igdir.edu.tr organization: Department of Software Engineering, Iğdır University, 76000, Iğdır, Turkey |
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| Cites_doi | 10.1016/j.amc.2020.125046 10.1002/mma.8649 10.2298/FIL1815433Y 10.3934/math.2024217 10.1002/mma.10375 10.1016/j.kjs.2023.12.007 10.1007/s13398-020-00903-6 10.7153/mia-2023-26-56 10.1016/j.aej.2024.07.015 10.31801/cfsuasmas.1537498 10.2298/FIL1804251R 10.1002/mma.5242 10.1155/2023/5245806 10.1155/2023/7457223 10.1007/s40314-024-02946-6 10.1109/TRO.2022.3187296 10.1002/mma.9636 10.3390/math9172141 |
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| Title | A comprehensive study on the shape properties of Kantorovich type Schurer operators equipped with shape parameter λ |
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