In this manuscript we introduce the notion of \((\alpha,\beta,\psi,\phi)\)-interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.

中文翻译：

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在 ( α , β , ψ , ϕ ) $(\alpha,\beta,\psi,\phi)$ - 插值收缩的设置下的不动点理论

在这份手稿中，我们引入了\((\alpha,\beta,\psi,\phi)\) -插值收缩的概念，它统一和概括了重要的概念：Proinov 型收缩、插值收缩和充足的频谱收缩。我们研究了保证此类映射不动点的存在性和唯一性的充分必要条件。