Recently Babu et al. [32] considered the class of mappings that satisfy 'condition (B)' as follows.
Example of mappings that satisfy Condition can be founded in [13].
They also discussed quasi-contraction, almost contraction and the class of mappings that satisfy condition (B) in detail.
Al-khaleel et al. [13] obtained several fixed point results for mappings that satisfy certain contractive conditions in generalized cone metric spaces.
In the following theorem, the existence of coincidence points of a hybrid pair of single-valued and multi-valued mappings that satisfy Suzuki-Zamfirescu hybrid contraction condition in partial metric spaces is established.
In this paper, we present common coincidence and common fixed point results for two pairs of mappings that satisfy the (E.A -property in thE.A -propertyrtinl methec setups.
A map f : X → X is said to satisfy 'condition (B)' if there exist a constant λ ∈ [ 0, 1 ) and some L ≥ 0 such that for all x, y ∈ X. d ( f x, f y ) ≤ λ d ( x, y ) + L min { d ( x, f x ), d ( y, f y ), d ( x, f y ), d ( y, f x ) }. Recently, Babu et al. [6] considered the class of mappings that satisfy 'condition (B)'.
Theorem 2.3 Let ( X, d, ⪯ ) be a complete partially ordered metric space, and let T, S X X → B ( X ) be two set-valued mappings that satisfy the property of generalized -weak contraction for all comparable x, y ∈ X, where (a) ψ is a continuous nondecreasing function with ψ ( t ) = 0 if and only if t = 0, (b) φ is a lower semicontinuous function with φ ( t ) = 0 if and only if t = 0. .
These results have been obtained by considering self-mappings that satisfy an explicit contractive-type condition.
The paper is organized as follows: in Section 2 we summarize some fixed point theorems for mappings satisfying Prešić type contractive conditions, in Section 3 we present the basic concepts and results concerning the stability of fixed point iteration procedures associated to self-mappings that satisfy explicit contractive conditions.
