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ϕ-contractive multivalued mappings in complex valued metric spaces and remarks on some recent papers

Authors :
Naval Singh
Vishal Joshi
Deepak Singh
Source :
Cogent Mathematics, Vol 3, Iss 1 (2016)
Publication Year :
2016
Publisher :
Informa UK Limited, 2016.

Abstract

The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via $ \phi $-contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers Ahmad, Klin-Eam, and Azam (2013) and Kutbi, Ahmad, Azam, and Al-Rawashdeh (2014) based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested.

Details

ISSN :
23311835
Volume :
3
Database :
OpenAIRE
Journal :
Cogent Mathematics
Accession number :
edsair.doi.dedup.....feeb2aaf47e30c3a3340171eba9e645a