In the present paper, we shall give an extension of the well known Pecaric-Rajic inequality in a quasi-Banach space, we establish the generalized inequality for an arbitrary number of finitely many nonzero elements of a quasi-Banach space, and obtain the corresponding upper and lower bounds. As a result, we get some more general inequalities.
Benyamini, Y. and Lindenstrauss, J. (2000) Geometric Nonlinear Functional Analysis. Vol. 1, Volume 48 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence, 65.