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\begin{document}$$q$$\end{document} be a prime power and Fq\documentclass[12pt]{minimal}
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\begin{document}$$ {{{\mathbb {F}}}}_q$$\end{document} be a finite field with q\documentclass[12pt]{minimal}
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\begin{document}$$q$$\end{document} elements. In this paper, we employ the AGW criterion to investigate the permutation behavior of some polynomials of the form b(xq+ax+δ)1+i(q2-1)d+c(xq+ax+δ)1+j(q2-1)d+L(x)\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} b(x^q+ax+\delta )^{1+\frac{i(q^2-1)}{d}}+c(x^q+ax+\delta )^{1+\frac{j(q^2-1)}{d}}+L(x) \end{aligned}$$\end{document}over Fq2\documentclass[12pt]{minimal}
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\begin{document}$$ {{{\mathbb {F}}}}_{q^2}$$\end{document} with a1+q=1,q≡±1(modd)\documentclass[12pt]{minimal}
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\begin{document}$$a^{1+q}=1, q\equiv \pm 1\pmod {d}$$\end{document} and L(x)=-ax\documentclass[12pt]{minimal}
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\begin{document}$$L(x)=-ax$$\end{document} or xq-ax.\documentclass[12pt]{minimal}
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\begin{document}$$x^q-ax.$$\end{document} Accordingly, we also present the permutation polynomials of the form b(xq+ax+δ)s-ax\documentclass[12pt]{minimal}
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\begin{document}$$b(x^q+ax+\delta )^s-ax$$\end{document} by letting c=0\documentclass[12pt]{minimal}
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\begin{document}$$c=0$$\end{document} and choosing some special exponent s, which generalize some known results on permutation polynomials of this form.
