Caristi’s Fixed Point Theorem in <i>G</i>-Cone Metric Spaces and Application

Some common fixed point theorems using G-Cone metric spaces with Banach algebra

“…Definition 2.4. [2] Let X be a non-empty set, A be a Banach algebra and G : X 3 → A be a function satisfying the following properties:…”

“…Definition 2.13. [2] Let (X, d) be a G-cone metric space over Banach algebra. G is said to be symmetric if…”

“…Definition 2.14. [2] A G-cone metric space over Banach algebra A is said to be G-bounded if for any x, y, z ∈ X, there exists K θ such that ||G(x, y, z)|| K Definition 2.15. [2] Let (X, G) be a G-cone metric space over Banach algebra and {x n } a sequence in X, c θ with c ∈ A.…”

“…More recently, Olaleru [14] proved some common fixed point theorems in cone metric spaces for weakly compatible mappings. Adewale [2] introduced the concept of G-cone metric spaces by replacing the set of real numbers with an ordered Banach space, proved convergence properties of sequences, and proved some fixed point theorems in this space. The concept of a G-cone metric space is more general than that of G-metric space and cone metric space.…”