Banas–Hajnosz–Wedrychowicz type modulus of convexity and normal structure in Banach spaces
In this paper, we present some sufficient conditions for which the Banach space X has uniform normal structure in terms of the Banas–Hajnosz–Wedrychowicz type modulus of convexity \(SY_X(\epsilon )\), the coefficient of weak orthogonality \(\omega (X)\) and the Domínguez–Benavides coefficient R(1, X). Some known results are improved and strengthened.
KeywordsBanas–Hajnosz–Wedrychowicz type modulus of convexity coefficient of weak orthogonality Domínguez–Benavides coefficient normal structure
Mathematics Subject ClassificationPrimary 46B20 Secondary 47H09
This research was partially supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ1601006), the Chongqing New-star Plan of Science and Technology (KJXX2017012), the Scientific Technological Research Program of the Chongqing Three Gorges University (no. 16PY11), the Chongqing Municipal Key Laboratory of Institutions of Higher Education (Grant no. 3), and the Program of Chongqing Development and Reform Commission (Grant no. 2017), the Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Georges University.
- 4.Gao, J.: Normal structure and modulus of \(U\)-convexity in Banach spaces, function spaces, differential operators and nonlinear analysis (Paseky and Jizerou, 1995), Prometheus, Prague, pp. 195-199 (1996)Google Scholar
- 5.Goebel, K., Kirk, W.: Topics in metric fixed point theory. In: Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1990)Google Scholar
- 13.Sims, B.: Ultra-techniques in Banach space theory. In: Queen’s Papers in Pure and Applied Mathematics, vol. 60. Queens University, Kingston (1982)Google Scholar