Some Moduli of Angles in Banach Spaces

Dandan Du, Asif Ahmad, Anwarud Din and Yongjin Li ()
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Dandan Du: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
Asif Ahmad: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
Anwarud Din: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
Yongjin Li: School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Mathematics, 2022, vol. 10, issue 16, 1-14

Abstract: In this paper, we mainly discuss the angle modulus of convexity δ X a ( ϵ ) and the angle modulus of smoothness ρ X a ( ϵ ) in a real normed linear space X , which are closely related to the classical modulus of convexity δ X ( ϵ ) and the modulus of smoothness ρ X ( ϵ ) . Some geometric properties of the two moduli were investigated. In particular, we obtained a characterization of uniform non-squareness in terms of ρ X a ( 1 ) . Meanwhile, we studied the relationships between δ X a ( ϵ ) , ρ X a ( ϵ ) and other geometric constants of real normed linear spaces through some equalities and inequalities. Moreover, these two coefficients were computed for some concrete spaces.

Keywords: angle modulus of convexity; angle modulus of smoothness; uniform non-squareness; geometric constant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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