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.
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Mercer, P.R. (2007) The Dunkl-Williams Inequality in an Inner Product Space. Mathematical Inequalities and Applications, 10, 447-450. https://doi.org/10.7153/mia-10-42
Pecaric, J. and Rajic, R. (2007) The Dunkl-Williams Equality in Pre-Hilbert C*-Modules. Linear Algebra and its Applications, 425, 16-25. https://doi.org/10.1016/j.laa.2007.03.005
Pecaric, J. and Rajic, R. (2007) The Dunkl-Williams Inequality with n Elements in Normed Linear Spaces. Mathematical Inequalities and Applications, 10, 461-470. https://doi.org/10.7153/mia-10-44
