Abstract
In this article, we define the concepts of $(\mathcal{F}^*,\varphi)$-contraction and $(\mathcal{F}^*,\varphi)$-expansion mappings in metric spaces and utilize the same to prove some $\varphi$-fixed point theorems for this kind of mappings. The obtained results used to present some results in partial metric spaces. Also, employing our newly results, we examine the existence and uniqueness of solution for integral equations. Furthermore supported example is provided.
Highlights
Wardowski [6] proved that every F-contraction mapping defined on a complete metric space admits a unique fixed point
T u = T v implies F(d(T u, T v)) ≥ F(d(u, v)) + τ, for all u, v ∈ X. Based on this definition Gornicki [22] presented some results for F-expansion mappings on metric and G-metric spaces
Let us recall the definition of partial metric space and other results given in [23]
Summary
Wardowski [6] proved that every F-contraction mapping defined on a complete metric space admits a unique fixed point. Let us recall the definition of partial metric space and other results given in [23]. A partial metric p on X is a mapping p : X ×X → [0, ∞) satisfying the following conditions (for all u, v, w ∈ X): (P1) p(u, u) = p(v, v) = p(u, v) ⇔ u = v; (P2) p(u, u) ≤ p(u, v); (P3) p(u, v) = p(v, u); (P4) p(u, v) ≤ p(u, w) + p(w, v) − p(w, w).
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