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In this paper, we define the modulus of $n$-dimensional $U$-flatness as the determinant of an $(n+1)\times(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.
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참고문헌 (12)
참고문헌 신청
B. Bollobas / 1970 / An extension to the theorem of Bishop and Phelps / Bull. London Math. Soc 2 : 181 ~ 182
B. Sims / 1982 / “Ultra”-techniques in Banach space theory / Queen’s University
D. Dacunha-Castelle / 1972 / Applications des ultraproduits a l’etude des espaces et des algebres de Banach / (French) Studia Math 41 : 315 ~ 334
J. Diestel / 1975 / Geometry of Banach spacesselected topics / Springer-Verlag
J. Gao / 2015 / The n-dimensional U-convexity and geometry of Banach spaces / J. Fixed Point Theory 16 (2) : 381 ~ 392
B. Sims / 1982 / “Ultra”-techniques in Banach space theory / Queen’s University
D. Dacunha-Castelle / 1972 / Applications des ultraproduits a l’etude des espaces et des algebres de Banach / (French) Studia Math 41 : 315 ~ 334
J. Diestel / 1975 / Geometry of Banach spacesselected topics / Springer-Verlag
J. Gao / 2015 / The n-dimensional U-convexity and geometry of Banach spaces / J. Fixed Point Theory 16 (2) : 381 ~ 392
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