Fixed point theorems via comparable mappings in ordered metric spaces
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In this paper, we introduce two new types of comparable multivalued mappings and prove a variant of well known classical Mizoguchi and Takahashi fixed point theorem for these mappings in partially ordered metric spaces. The method we use in the proof of our results is technically connected with the proof given by Suzuki (J Math Anal Appl 340:752–755, 2008). We also provide examples to vindicate our claims and usability of the present results.
KeywordsFixed point Partially ordered set Comparable multivalued mappings
Mathematics Subject Classification47H10 54H25
The authors thank the referees for their careful reading of the manuscript and insightful comments.
All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.
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Conflict of interest
All the authors declare that there is no conflict of interests.