On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions

Abstract

In this article we have introduced the sequence space $m(\phi,d)$ and $m(M,\phi,d)$ of W. L. C. Sargent type in a metric space $(X, d)$ on generalising the sequence space $m(\phi)$ and we have defined these sequence spaces using the Orlicz function $M$. We have investigated their different properties like solidness, symmetricity, monotone, sequence algebra, completeness etc. We have established some inclusion results involving the space $m(M,\phi,d)$ and some of the existing sequence spaces. We have provided suitable examples and discussed in detail, in order to justify the failure cases and the definitions we have introduced. The results established in this article generalized and unifies several existing results.

Keywords

• metric space
• orlicz function
• $p$-absolutely summable sequences
• solid space
• symmetric space