On the iterative scheme generating methods using mean-valued sequences

Using the Mann method and the shrinking projection method, we present generalized forms of iterative scheme generating methods and compared them with prior frameworks. To this end, the properties of mean-valued sequences are leveraged. Subsequently, we establish a convergence theorem similar to that developed by Martinez-Yanes and Xu. This approach highlights the difference between the conventional shrinking projection method and the Martinez-Yanes and Xu variant. The proposed frameworks yield various types of iterative schemes for finding common fixed points, including a three-step
iterative scheme. The class of mappings considered incorporate general types, including nonexpansive mappings.