Some New Results in Partial Cone $b$-Metric Space

Abstract

In this paper, we introduce the concepts of the Ulam-Hyers-Rassias stability and the limit shadowing property of a fixed point problem and the $P$-property of a mapping in partial cone $b$-metric space. Also, we give such results by using the mapping which is studied by Fernandez et al.[4] in partial cone $b$-metric space and provide some numerical examples to support our results. The results presented here extend and improve some recent results announced in the current literature.

Keywords

• fixed point
• limit shadowing property
• p-property
• partial cone b-metric space
• ulam-hyers-rassias stability