Monotonicity and extremality analysis of difference operators in Riemann-Liouville family

Pshtiwan Othman Mohammed, Dumitru Baleanu, Thabet Abdeljawad, Eman Al-Sarairah, Y. S. Hamed

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageBritish English
Pages (from-to)5303-5317
Number of pages15
JournalAIMS Mathematics
Volume8
Issue number3
DOIs
StatePublished - 2023

Keywords

  • extremality analysis
  • monotonicity analysis
  • Riemann-Liouville discrete operators

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