A Remark and an Improved Version on Recent Results Concerning Rational Functions

Key Points

• The refinement of the Turán-type inequality offers improved bounds for rational functions, enhancing clarity in results.
• A lemma extending earlier work allows for a more comprehensive understanding of inequalities related to rational functions.
• The paper discusses applications through examples, demonstrating the significance of the auxiliary result in extending previous conclusions.
• The findings build upon recent research by Akhter et al., advancing insights in the field of rational functions.