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Orlicz lacunary sequence spaces of l-fractional difference operators

Raj Kuldip, Saini Kavita, Choudhary Anu

Journal of Applied Analysis

2020

Vol. 26, nr 2

173--183

Recently, S. K. Mahato and P.D. Srivastava [A class of sequence spaces defined by l-fractional difference operator, preprint (2018), http://arxiv.org/abs/1806.10383] studied l-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda l-fractional convergent, lambda l-fractional null and lambda l-fractional bounded sequences over n-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

The new investigation of the stability ofmixed type additive-quartic functionalequations in non-Archimedean spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

2020

Vol. 53, nr 1

174--192

In this article, we prove the generalized Hyers-Ulam stability for the following additive-quarticfunctional equation: f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) + 24f(y) = 13[ f(x + y) + f(x - y)] + 12f(2y), where f maps from an additive group to a complete non-Archimedean normed space.