Rao et al. Fixed Point Theory and Applications (2017) 2017:17
R E S E A R C H Open Access
Applications and common coupled ﬁxed
point results in ordered partial metric spaces
, Kenan Tas
, S Satyanaraya
and D Ram Prasad
Department of Computing, Adama
Science and Technology University,
Full list of author information is
available at the end of the article
In this paper, we obtain a unique common coupled ﬁxed point theorem by using
)-contraction in ordered partial metric spaces. We give an application to
integral equations as well as homotopy theory. Also we furnish an example which
supports our theorem.
Keywords: partial metric; w-compatible maps; coupled ﬁxed point; mixed
contraction; homotopy theory
the study of denotational semantics of data ﬂow networks. In fact, it is widely recognized
that PMSs play an important role in constructing models in the theory of computation
and domain theory in computer science (see e.g. [–]).
Matthews [, ], Oltra and Valero  and Altun et al. provedsomeﬁxedpoint
theorems in PMSs for a single map. For more work on ﬁxed, common ﬁxed point theorems
in PMSs, we refer to [, –].
The notion of a coupled ﬁxed point was introduced by Bhaskar and Lakshmikantham
 and they studied some ﬁxed point theorems in partially ordered metric spaces. Later
some authors proved coupled ﬁxed and coupled common ﬁxed point theorems (see [,
The aim of this paper is to study unique common coupled ﬁxed point theorems of Jungck
type maps by using a (ψ, α, β)-contraction condition over partially ordered PMSs.
First we recall some basic deﬁnitions and lemmas which play a crucial role in the theory
Deﬁnition . (See [, ]) A partial metric on a non-empty set X is a function p : X ×X →
such that, for all x, y, z ∈ X,
) x = y ⇔ p(x, x)=p(x, y)=p(y, y),
) p(x, x) ≤ p(x, y), p(y, y) ≤ p(x, y),
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