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Let  ÃŽÂ´X(ÃÂµ) and R(1,X) be the modulus of convexity and the DomÃƒÂ­nguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space X has normal structure if  2ÃŽÂ´X(1+ÃÂµ)>max{(R(1,x)-1)ÃÂµ,1-(1-ÃÂµ/R(1,X)-1)} for some ÃÂµÃ¢ÂˆÂˆ[0,1] which generalizes the known result by Gao and Prus

abstract and applied analysis

Modulus of Convexity, the Coeffcient<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>X</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, and Normal Structure in Banach Spaces

Modulus of Convexity, the CoeffcientR(1,X), and Normal Structure in Banach Spaces