On some n-normed sequence spaces

Abstract

In this work, we applied a new method for solving the linear weakly singular mixed Volterra-Fredholm integral equations. We now begin the theoretical study with acquirement of the variational form; in addition, we are using Bernstein spectral Galerkin method to be approximate to my problems. We estimate the error of the method by proved some theorems. Moreover, in the final section, we solved some numerical examples.

Strong convergence for the modified Mann’s iteration of λ-strict pseudocontraction

“…Our main results are obtained in the frame of q−uniformly smooth Banach space, then in the future work, we may consider the results of this paper in n−Banach space. For more details on n−Banach space, see Dutta [2,3,4,5,6,7,8,9,10].…”

A-contraction mappings of integral type in n-normed spaces

“…This n-norm is defined by using the set of bounded linear functionals on X. Since then, many researchers have studied operators and functionals on n-normed space X (see [2,3,4,5,6,7,8,9,10,11,12]). In [5], Pangalea and Gunawan introduced the concept of n-dual spaces and proved that for every real normed space X of dimension d ≥ n, there are two n-dual spaces associated to X.…”

“…Also reproved the Cauchy-Schwarz inequality and gave a necessary and sufficient condition for the equality. Dutta and Mazaheri [9], introduced the idea of constructing sequence spaces with elements in an n-norm space in comparison with the spaces 0 , c, ∞ and the Orlicz space and extended the notion of n-norm to such spaces. Also, stated and defined some statements about the n-best approximation in nnormed spaces.…”