【摘要】 Banach空间X的许多几何性质在不动点理论中都具有重要的作用,1997年,Garcia Falset证明了当R(X)<2时,Banach空间X具有不动点性质.本文通过研究了Banach空间X的(L)性质与Opial性质,一致Opial性质,Non strictOpial性质及R(X)几何常数之间的关系,得出了(L)性质与一致Opial性质的等价条件,并得到自反且具有一致Opial性质的Banach空间X具有不动点性质.更多还原

【Abstract】 In Banach spaces, there are many geometric properties that play important roles in fixed point theory. In 1997, Garcia-Falset proved that when R(X)<2, a Banach space has X the fixed point property.In this paper, we study the relation between (L) property, Opial property, Non-strict Opial property and R(X) geometric constant in Banach space X. We get some equivalent conditions of (L) property and uniform Opial property. Moreover, we prove that reflexive Banach space with uniform Opial property has fixed point property.更多还原