Fixed Point Theorems for Some Iteration Processes with Generalized Zamfirescu Mappings in Uniformly Convex Banach Spaces

Abstract

This paper establishes fixed point theorems for certain iteration processes in uniformly convex Banach spaces using generalized Zamfirescu mappings. The results improve upon recent findings in the literature. The study focuses on iterative schemes such as Mann and Ishikawa, demonstrating their strong convergence to fixed points under generalized Zamfirescu contractive conditions. The work contributes to the broader understanding of fixed point theory in uniformly convex Banach spaces and provides a foundation for further research in this area.