Abstract
In this paper, first, we deal with new metric space Sm-metric space that combines multiplicative metric space and S-metric space. We generate a common fixed point theorem in a Sm-metric space using the notions of reciprocally continuous mappings, faintly compatible mappings and occasionally weakly compatible mappings (OWC). We are also studying the well-posedness of Sm metric space. Further, some examples are presented to support our outcome.
Highlights
The idea of Multiplicative metric space(MMS for short ) was first introduced by Bashirove [1] in 2008.Ozaksar and Cevical [2] investigated and proved the properties of multiplicative metric space (MMS)
We generate a common fixed point theorem in a Sm-metric space using the notions of reciprocally continuous mappings, faintly compatible mappings and occasionally weakly compatible mappings (OWC)
We used the concept of occasionally weakly compatible (OWC for shot) [9]mappings, reciprocally continuous and faintly compatible mappings [10] to generate a common fixed point theorem in Sm-metric space
Summary
The idea of Multiplicative metric space(MMS for short ) was first introduced by Bashirove [1] in 2008.Ozaksar and Cevical [2] investigated and proved the properties of MMS. Sedhi.S et al [5] introduced a new structure of S-metric space and developed some fixed point theorems. We use the multiplicative metric space and S metric space and generated a new Sm-metric space [7]. We used the concept of occasionally weakly compatible (OWC for shot) [9]mappings, reciprocally continuous and faintly compatible mappings [10] to generate a common fixed point theorem in Sm-metric space. Multiplicative metric space; S-metric space; Sm-metric space; occasionally weakly compatible; reciprocally continuous; faintly compatible mappings; well-posed property
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