We propose and analyze a new inertial type iterative algorithm for finding a common solution of generalized mixed variational-like inequality problem, variational inequality problem for a \(\gamma \)-inverse strongly monotone mapping and fixed point problem for a asymptotically quasi-\(\phi \)-nonexpansive mapping in the framework of two-uniformly convex and uniformly smooth real Banach space. Further, we prove that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of these problems. Furthermore, we give some consequences of the main result. Finally, we discuss some numerical examples to demonstrate the applicability of the iterative algorithm. The results presented in this paper unify and extend some known results in this area.

我们提出并分析了一种新的惯性类型迭代算法，以找到广义混合类似变分不等式问题，\（\ gamma \）逆强单调映射的变分不等式问题和渐近拟\\不动点问题的通用解。（\ phi \） -在两个一致凸且一致平滑的实Banach空间的框架中的非扩张映射。此外，我们证明了所提出的迭代算法生成的序列强烈收敛于这些问题的通用解决方案。此外，我们给出了主要结果的一些后果。最后，我们讨论一些数值示例，以证明迭代算法的适用性。本文介绍的结果统一并扩展了该领域中的一些已知结果。