Abstract
The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.
Highlights
Matthews [1] introduced partial metric spaces as a part of the study of denotational semantics of data flow networks
The usual metric was replaced by partial metric, with a property that the self-distance of any point may not be zero
It is widely recognized that partial metric spaces play an important role in constructing models in the theory of computation
Summary
Matthews [1] introduced partial metric spaces as a part of the study of denotational semantics of data flow networks. Banach contraction principle ensures the existence and uniqueness of a fixed point of a contractive self-map of metric space and has many applications in applied sciences. The fixed point result of Matthews is the generalization of the following Banach contraction principle. The fixed point result of Matthews is generalized by several authors for single self map in partial metric spaces (see, e.g., [4,5,6]). The purpose of this paper is to prove some common fixed point theorems for a sequence of self maps on partial metric spaces and generalize the result of Matthews. The notion of asymptotically regular mapping in partial metric spaces is introduced and a fixed point result for the mappings of this class is proved
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