Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212120210501Anti-N-order polynomial Daugavet property on Banach spaces10971105497510.22075/ijnaa.2019.16371.1865ENJohn EmenyuDepartment of Mathematics, Faculty of Science, Mbarara University of Science and Technology, UgandaJournal Article20181031We generalize the notion of the anti-Daugavet property (a-DP) to the anti-N-order polynomial Daugavet property (a-NPDP) for Banach spaces by identifying a good spectrum of a polynomial and prove that locally uniformly alternatively convex or smooth Banach spaces have the a-mDP for rank-1 polynomials. We then prove that locally uniformly convex Banach spaces have the a-NPDP for compact polynomials if and only if their norms are eigenvalues, and uniformly convex Banach spaces have the a-NPDP for continuous polynomials if and only if their norms<br />belong to the approximate spectra.https://ijnaa.semnan.ac.ir/article_4975_dcbcd4a6a92b6b490dbbbb5250a63af9.pdf