A. Qazi, Mohammed2024-07-122024-07-122019A. Qazi, M. (2019). An inequality for self reciprocal polynomials. International Conference of Mathematical Sciences (ICMS 2019). s. 48.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2140Let Pn be the class of all polynomials of degree at most n. Polynomials f ? Pn which satisfy the condition z nf(1/z) ? f(z) are called self-reciprocal and form the sub-class P ? n of Pn. For any ? > 0, let M?(f ; ?) := max|z|=? |f(z)| and Mp(f ; ?) := ( 1 2? ? ? ?? |f(?e i? )| p d? )1/p , 0 < p < ?. If f ? Pn then Mp(f ? ; ?) ? n?n?1 Mp(f ; 1) for any p > 0 and ? ? 1, whereas, if f ? P? n then Mp(f ? ; ?) ? (n/2)? n?1 Mp(f ; 1) for any p > 0 and ? ? 1. Lately, it has been noted that at least for p ? 1, there exists a positive number ?n strictly less than 1 such that Mp(f ? ; ?) ? n?n?1 Mp(f ; 1) for ? ? ?n if f ? Pn. By analogy, it has been asked if there was a positive number ? ? n < 1 such that Mp(f ? ; ?) ? (n/2)? n?1 Mp(f ; 1) for all ? ? ? ? n and any f ? P? n. We propose to discuss this question.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessPolynomialsBernstein’s inequalityZygmund’s inequalityArticle4848