We introduce the q-paranorm, investigate some of its properties. We further give an algorithm which constructs the best linear approximations under the q-paranorm.

The main purpose of this paper is to use the idea of n-norm and a modulus function to construct some multiplier sequence spaces with base space X, a real linear n-norm space. We study the spaces for linearity, existence of paranorm, completeness and some inclusion properties involving these spaces. Mathematics Subject Classification: 40A05, 46A45, 46E30

ABTRACT: In this paper we define the generalized Cesaro sequence spaces ces(p, q, s). We prove the space ces(p, q, s) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual. In section-3 we establish necessary and sufficient conditions for a matrix A to map ces p, q, s to l∞ and ces(p, q, s) to c, where l∞ is the space of all bounded sequences and c is the space of all ...

In this paper we define the weighted Cesaro sequence spaces ces (p, q).We prove the space ces(p, q) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual and continuous dual. In section-3 we establish necessary and sufficient condition for a matrix A to map ces (p, q) to and ces(p, q) to , where is the space of all bounded sequences and is the space of all convergent s...

Let l∞ and c denote the Banach spaces of bounded and convergent sequences x = (xk), with xk ∈R or C, normed by ‖x‖ = supk |xk|, respectively. A paranorm on a linear topological space X is a function g : X →R which satisfies the following axioms for any x, y,x0 ∈ X and λ,λ0 ∈ C: (i) g(θ) = 0, where θ = (0,0,0, . . .), the zero sequence, (ii) g(x) = g(−x), (iii) g(x+ y) ≤ g(x) + g(y) (subadditivi...

and Applied Analysis 3 2. The Sequence Space λ, p In this section, we define the sequence space λ, p and prove that this sequence space according to its paranorm is complete paranormed linear space. In 1 , Mursaleen and Noman defined the matrix Λ λnk ∞ n,k 0 by λnk ⎧ ⎨ ⎩ λk − λk−1 λn 0 ≤ k ≤ n 0 k > n , 2.1 where λ λk ∞ k 0 is a strictly increasing sequence of positive reals tending to ∞, that ...

in the present paper we define strongly δn -summable sequences which generalize a-summablesequences and prove such spaces to be complete paranormed spaces under certain conditions, sometopological results have also been discussed.