I n this paper, we give several new characterizations of 2-inner product spaces and strict convexity for linear 8-normed spaces in terms of orthogonalites and 2-semi-inner product spaces = (s+y), and scalar multiplication (tlz),=a(x),. For arbitrary z, y in X with (~),=(y),, 1 1 5 , cll=lly, cll since 1 1 1 5 , c~~--~~y , cII I ~l l z -y , clj =O. Therefore, the function 11-l [, on X , defined by ~~( x ) ,~\ , =~] z , cII is well-defined and is a norm on X, ([4]).The notion of a %semi-inner product was introduced by S. RIZVI and A. SIDDIQUI ([22]). But Y. Ho and A. WHITE ([15]) modified one part, (Sl), of their definition and then stated and proved their theorems with the modified definition.Let [.; I -1 be a real valued function on X x X x X satisfying the following condi-
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