Some Stability Results for Picard Iterative Process in Uniform Space
نویسنده
چکیده
The following concepts shall be required in the sequel: Definition 1.1 [5, 27]. A uniform space (X,Φ) is a nonempty set X equipped with a nonempty family Φ of subsets of X ×X satisfying the following properties: (i) if U is in Φ, then U contains the diagonal {(x, x) |x ∈ X}; (ii) if U is in Φ and V is a subset of X ×X which contains U, then V is in Φ; (iii) if U and V are in Φ, then U ∩ V is in Φ; (iv) if U is in Φ, then there exists V in Φ, such that, whenever (x, y) and (y, z) are in V, then (x, z) is in U ; (v) if U is in Φ, then {(y, x) |(x, y) ∈ U} is also in Φ. Φ is called the uniform structure of X and its elements are called entourages or neighbourhoods or surroundings. The space (X,Φ) is called quasiuniform if property (v) is omitted. The notions of an A-distance and an E-distance were introduced by Aamri and El Moutawakil [1] to prove some common fixed point theorems for some new contractive or expansive maps in uniform space. In [1], the following contractive definition was employed: Let f, g : X → X be selfmappings of X. Then, we have
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