Quasi Contraction and Fixed Points

Roohi, Mehdi; Alimohammady, Mohsen

doi:10.5899/2012/jnaa-00168

Cited by 1 publication

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“…Of note is the generalization of Nadler [11] to multifunctions on metric spaces satisfying a contraction condition. Some recent treatments and extensions/generalizations of fixed point theorems for multivalued functions are given in [14] and [12]. Significant research has been undertaken recently on the study of fixed point theorems in partial metric spaces (see, for instance, recent work by Alghamdi et al [1]).…”

Section: Introductionmentioning

confidence: 99%

A Fixed Point Theorem for Multifunctions in Partial Metric spaces

Macansantos¹

2013

Journal of Nonlinear Analysis and Application

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Fixed Point theorems on partial metric spaces have been the subject of recent work, with the interest generated in partial metric spaces (as a suitable structure for studies in theoretical computer science). Several approaches to fixed point theory for point-valued functions on complete metric spaces have been generalized to partial metric spaces (see, for instance, Alghamdi [1]). On the other hand, it appears that substantial work may still be done to generalize the theory (in the partial metric space context) to set-valued functions. Recently, Damjanovic et al [3] looked into pairs of multi-valued and single-valued maps in complete metric spaces, and used coincidence and common fixed points, to establish a theorem on fixed points for pairs of multivalued functions. In this paper we take off from Damjanovic and proceed to establish the same result in the setting of partial metric spaces. As a consequence of our generalization, we are able to include as special cases the theorem of Aydi et al [2] and our [9] generalization of [4]. Further, Reich's result is also generalized to multivalued functions in partial metric spaces. Special cases include the partial metric space version of Kannan's theorem, as well as that due to Hardy and Rogers.

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Section: Introductionmentioning

confidence: 99%

A Fixed Point Theorem for Multifunctions in Partial Metric spaces

Macansantos¹

2013

Journal of Nonlinear Analysis and Application

View full text Add to dashboard Cite

show abstract

Quasi Contraction and Fixed Points

Cited by 1 publication

References 15 publications

A Fixed Point Theorem for Multifunctions in Partial Metric spaces

A Fixed Point Theorem for Multifunctions in Partial Metric spaces

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