We say that those mappings which satisfy the above relation map the domain Ω strictly inside itself.
In this paper, we delete the continuity of the mappings and obtain some fixed point theorems for one expanding mapping and introduce common fixed point theorems for two expanding mappings, which satisfy generalized expansive conditions in nonnormal cone metric spaces.
The following example shows that there are discontinuous mappings which satisfy the conditions of Theorem 2.2.
They also established coupled fixed point theorems for mappings which satisfy the mixed monotone property.
Babu et al. introduced in [8] the class of mappings which satisfy 'condition (B)'.
For some examples of mappings which satisfy we refer to [7].
In Section 3 of this paper, we will give an important example of sequence of -Lipschitzian mappings which satisfies the (SU) condition.
Recently, Ćirić and Ume [49] defined a wide class of multi-valued non-self-mappings which satisfy a generalized contraction condition and proved a fixed point theorem which generalizes the results of Itoh [50] and Khan [51].
(iv) If is a complete metric space, then there is a unique set satisfying ; with for any and any given. . ; are all composed -cyclic -contraction self-mappings which satisfy, in addition, ; (i.e., and ; ) and which possess common fixed points in, that is, ;.
Then, the following properties hold provided that ;. (i) ; are all composed -cyclic -contraction self-mappings which satisfy, in addition, ; (i.e., and ; ) and which possess common fixed points in, that is, ;. (ii) There is a unique set satisfying the constraints, subject to, for any given and for any given.
Corollary 1 Suppose that g is a nondecreasing self-map on X and F : X → X and g : X → X are self-mappings which satisfy f ( p ( F x, F y ) ) ≤ ψ ( f ( M g ( x, y ) ) ). for any ( x, y ) ∈ Δ g, where f ∈ Ϝ s, ψ ∈ Φ and M g ( x, y ) = max { p ( g x, g y ), p ( F x, g x ), p ( F y, g y ), p ( F x, g y ) + p ( F y, g x ) 2 }.
