Abstract
Abstract Some common fixed point theorems for a family of non-self mappings defined on a closed subset of a metrically convex cone metric space (over the cone which is not necessarily normal) are obtained which generalize earlier results due to Imdad et al. and Janković et al. MSC:47H10, 54H25.
Highlights
Introduction and preliminariesThe existing literature of fixed point theory contains many results enunciating fixed point theorems for self-mappings in metric and Banach spaces
Fixed point theorems for non-self mappings are not frequently discussed and so they form a natural subject for further investigation
The study of fixed point theorems for non-self mappings in metrically convex metric spaces was initiated by Assad and Kirk [ ]
Summary
Since {Tx nk } is a Cauchy sequence in TC, it converges to a point z ∈ TC. {Sx nk+ } being a subsequence of the Cauchy sequence {Tx , Sx , Tx , Sx , . Since the Cauchy sequence {Tx nk } converges to z ∈ C and z = Fiw, z ∈ FiC ∩ C ⊆ SC, there exists v ∈ C such that Sv = z. If we assume that there exists a subsequence {Sx nk+ } ⊆ Q with TC as well as SC closed in X, noting that {Sx nk+ } is a Cauchy sequence in SC, foregoing arguments establish (IV) and (V). Fiz = z = Tz. we can prove Fjz = z = Sz. z = Fiz = Fjz = Sz = Tz, that is, z is a common fixed point of Fn, S and T. Define Fi, Fj, S and T : C → X as
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