Abstract
In this paper, we introduce a new concept of partial rectangular metric-like space and prove some results on the existence and uniqueness of a fixed point of a functionT:X⟶X, defined on a partial rectangular metric-like spaceX, which fulfills a nonlinear contractive condition using a comparison function and the diameter of the orbits. The obtained results generalize some previously acknowledged results in partial metric spaces, partial rectangular metric spaces, and rectangular metric-like spaces. The examples presented prove the usefulness of the introduced generalizations.
Highlights
Fixed point theory has a wide application in functional analysis
Partial metric spaces were introduced by Mathew [6] in 1994
He studied their topologies and presented a result relying on the fixed points in these spaces related to Banach contraction. ese results had been generalized subsequently by many other studies [7,8,9,10,11]
Summary
Fixed point theory has a wide application in functional analysis. Various authors [1,2,3,4,5] have contributed to this field expanding the metric spaces by changing their axioms or by improving the contractive conditions.Partial metric spaces were introduced by Mathew [6] in 1994. A function d: X × X ⟶ R+ is a rectangular metric on X if for every x, y ∈ X and for all distinct points u, v ∈ X − x, y, it satisfies the following conditions: (i) (R1) x y if and only if d(x, y) 0 (ii) (R2) d(x, y) d(y, x) (iii) (R3) d(x, y) ≤ d(x, u) + d(u, v) + p(v, y)
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