In this article we introduce some vector valued difference paranormed double sequence spaces defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

*Correspondence: [email protected] 1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Abstract In this paper, we characterize the matrix classes ( 1, p(F)) (1≤ p <∞), where p(F) is some Fibonacci di...

In this study, we define the spaces fs(u, v,4), f(u, v,4) and f0(u, v,4) that consist of all sequence whose G(u, v,4)− transforms are in the set of almost convergent sequence and series spaces. Some topological properties of the new almost convergent sets have been investigated as well as γand β-duals of the spaces f(u, v,4) and fs(u, v,4). Also, the characterization of certain matrix classes o...

In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of fin...