Abstract
Abstract We establish common fixed point results for two pairs of weakly compatible mappings on a partial metric space, satisfying a weak contractive condition involving generalized control functions. The presented theorems extend and unify various known fixed point results. Examples are given to show that our results are proper extensions of the known ones. MSC:47H10, 54H25, 54H10.
Highlights
1 Introduction In [ ], Matthews introduced the notion of a partial metric space as a part of the study of denotational semantics of dataflow networks
Altering distance functions were introduced by Khan et al [ ]. They were used by many authors to obtain fixed point results, including those in partial metric spaces (e.g., Abdeljawad [ ], Abdeljawad et al [, ], Altun et al [ ], Ćirić et al [ ], Karapinar and Yüksel [ ])
Generalized altering distance functions with several variables were used on metric spaces by Berinde [ ], Choudhury [ ] and Rao et al [ ]
Summary
In [ ], Matthews introduced the notion of a partial metric space as a part of the study of denotational semantics of dataflow networks. They were used by many authors to obtain fixed point results, including those in partial metric spaces (e.g., Abdeljawad [ ], Abdeljawad et al [ , ], Altun et al [ ], Ćirić et al [ ], Karapinar and Yüksel [ ]). Generalized altering distance functions with several variables were used on metric spaces by Berinde [ ], Choudhury [ ] and Rao et al [ ]. An attempt has been made to derive some common fixed point theorems for two pairs of weakly compatible mappings on partial metric spaces, satisfying a weak contractive condition involving generalized control functions.
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