Summary: In this article we introduce the sequence spaces \([\chi_f^{3FI},||(d(x_1), d(x_2),\dots,d(x_{n-1})||_p]\) and \([\Lambda_f^{3FI},||(d (x_1),d(x_2),\dots,d(x_{n-1})||_p]\), and study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces and some of their properties like solidity, symmetricity, convergence free etc., and also investigate some inclusion relations related to these spaces.