In this paper, the convergence and dynamics of improved Chebyshev-Secant-type iterative methods are studied for solving nonlinear equations in Banach space settings. Their semilocal convergence is established using recurrence relations under weaker continuity conditions on first-order divided differences. Convergence theorems are established for the existence-uniqueness of the solutions. Next, center-Lipschitz condition is defined on the first-order divided differences and its influence on the domain of starting iterates is compared with those corresponding to the domain of Lipschitz conditions. Several numerical examples including Automotive Steering problems and nonlinear mixed Hammerstein-type integral equations are analyzed, and the output results are compared with those obtained by some of similar existing iterative methods. It is found that improved results are obtained for all the numerical examples. Further, the dynamical analysis of the iterative method is carried out. It confirms that the proposed iterative method has better stability properties than its competitors.

本文研究了改进的Chebyshev-Secant型迭代方法在Banach空间设置中求解非线性方程的收敛性和动力学。它们的半局部收敛是使用一阶分割差的较弱连续性条件下的递归关系建立的。建立收敛定理以求解的存在唯一性。接下来，在一阶除法差上定义中心Lipschitz条件，并将其对起始迭代域的影响与与Lipschitz条件域对应的影响进行比较。分析了几个数值示例，包括汽车转向问题和非线性混合Hammerstein型积分方程，并将输出结果与通过某些类似的现有迭代方法获得的结果进行比较。发现对于所有数值示例都获得了改进的结果。此外，进行了迭代方法的动力学分析。它证实了所提出的迭代方法比其竞争者具有更好的稳定性。