Journal of Theoretical Physics & Mathematics Research

Fixed Point Theorems for Berinde-type Contractions in Cone Banach Spaces via a Tri-Inertial Split-Averaged λ-Iteration and Applications

Abstract

Elvin Rada

We establish new fixed point theorems in cone Banach spaces using a tri-Inertial split-averaged λ-iteration process. Our results focus on Berinde-type weak contractions and common fixed points for compatible mappings. The new iteration generates three auxiliary sequences and improves convergence speed and stability compared to classical schemes. We provide error estimates and convergence rates, extending classical results. Applications to nonlinear integral and differential equations demonstrate the effectiveness of the proposed approach, which we denote as TISA-λ-iteration.

PDF