Monotonicity and extremality analysis of difference operators in Riemann-Liouville family
Date
2023
Authors
Mohammed, Pshtiwan Othman
Baleanu, Dumitru
Abdeljawad, Thabet
Al-Sarairah, Eman
Hamed, Y.S.
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Abstract
In this paper, we will discuss the monotone decreasing and increasing of a discrete nonpositive and nonnegative function defined on Nr0 +1, respectively, which come from analysing the discrete Riemann-Liouville differences together with two necessary conditions (see Lemmas 2.1 and 2.3). Then, the relative minimum and relative maximum will be obtained in view of these results combined with another condition (see Theorems 2.1 and 2.2). We will modify and reform the main two lemmas by replacing the main condition with a new simpler and stronger condition. For these new lemmas, we will establish similar results related to the relative minimum and relative maximum again. Finally, some examples, figures and tables are reported to demonstrate the applicability of the main lemmas. Furthermore, we will clarify that the first condition in the main first two lemmas is solely not sufficient for the function to be monotone decreasing or increasing.
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Keywords
Extremality Analysis, Monotonicity Analysis, Riemann-Liouville Discrete Operators
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Citation
Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and extremality analysis of difference operators in Riemann-Liouville family", AIMS Mathematics, Vol.8, No.3, pp.5303-5317.
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Source
AIMS Mathematics
Volume
8
Issue
3
Start Page
5303
End Page
5317