Let s be a prime power and $$ {{{\mathbb {F}}}}_q$$ be a finite field with s elements. In this paper, we employ the AGW criterion to investigate the permutation behavior of some polynomials of the form $$\begin{aligned} b(x^q+ax+\delta )^{1+\frac{i(q^2-1)}{d}}+c(x^q+ax+\delta )^{1+\frac{j(q^2-1)}{d}}+L(x) \end{aligned}$$over $$ {{{\mathbb {F}}}}_{q^2}$$ with $$a^{1+q}=1, q\equiv \pm 1\pmod {d}$$ and $$L(x)=-ax$$ or $$x^q-ax.$$ Accordingly, we also present the permutation polynomials of the form $$b(x^q+ax+\delta )^s-ax$$ by letting $$c=0$$ and choosing some special exponent s, which generalize some known results on permutation polynomials of this form.

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更正：某些类别的置换多项式形式 $$b(x^q+ax+\delta )^{\frac{i(q^2-1)}{d}+1}+c(x^q+ ax+\delta )^{\frac{j(q^2-1)}{d}+1}+L(x)$$ 超过 $$ \mathbb{F}_{q^2}$$

设 s 为质数幂，$$ {{{\mathbb {F}}}}_q$$ 为具有 s 个元素的有限域。在本文中，我们采用 AGW 准则来研究 $$\begin{aligned} b(x^q+ax+\delta )^{1+\frac{i(q^2- 1)}{d}}+c(x^q+ax+\delta )^{1+\frac{j(q^2-1)}{d}}+L(x) \end{aligned}$$超过 $$ {{{\mathbb {F}}}}_{q^2}$$ 与 $$a^{1+q}=1, q\equiv \pm 1\pmod {d}$$ 和 $ $L(x)=-ax$$ 或 $$x^q-ax.$$ 相应地，我们还提出了 $$b(x^q+ax+\delta )^s-ax$$ 形式的置换多项式通过让 $$c=0$$ 并选择一些特殊的指数 s，它概括了这种形式的置换多项式的一些已知结果。