Let \((X, \left\langle \cdot \right\rangle )\) be a Hilbert space and \(T:X\rightarrow X\) be a decreasing operator. Under a metric condition involving the convex combination of x and T(x), we will prove some fixed point theorems which generalize and complement several results in the theory of nonlinear operators. Our results are closely related to the admissible perturbations approach in fixed point theory.

中文翻译：

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希尔伯特空间中减少凸轨道算子的不动点结果

令\((X, \left\langle \cdot \right\rangle )\)是一个希尔伯特空间，而\(T:X\rightarrow X\)是一个递减运算符。在涉及x和T ( x )的凸组合的度量条件下，我们将证明一些不动点定理，这些定理对非线性算子理论中的几个结果进行了推广和补充。我们的结果与不动点理论中的可容许扰动方法密切相关。