Abstract

 In this paper we introduce the notion of the Multiplicative Semi-Metric Space and proved common fixed point theorems. We establish fixed point theorems for four self-maps which can be extended to derive common fixed point theorems involving any finite number of mappings in Multiplicative Semi Metric Space. Further examples are discussed to show that compatible mappings of type-E, weakly compatible mappings and reciprocally-continuous mappings are weaker forms of compatible mappings and continuous mappings respectively. The main objective of this article is to prove the unique common fixed point theorems and employing the notion of the compatible mappings of type-E, reciprocally-continuous mappings in the Multiplicative Semi Metric Space. Our result generalizes the concept of Multiplicative Metric Space as it does not involve the multiplicative triangle inequality.
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