What does this research mean for the field?

The novel iterative algorithm C_{SA}IA achieves △-convergence to a common fixed point for two quasi non-expansive operators with property (E) in CAT(0) spaces. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to develop an iterative algorithm to find common fixed points in CAT(0) spaces using quasi non-expansive mappings.

June 1, 2026Open Access

Common fixed point results via Cₒ₀IA using quasi non-expansive mappings in CAT (0) spaces

Key Points

The aim is to develop an iterative algorithm to find common fixed points in CAT(0) spaces using quasi non-expansive mappings.
Developed a novel iterative algorithm, C_SAIA.
Applied the algorithm to demonstrate △-convergence for operators D and C.
Detailed lemmas and theorems provide the theoretical foundation for the algorithm.
Demonstrated △-convergence to a common fixed point for two operators in CAT(0) space.
Established theoretical lemmas that support the convergence claims.
Presented a numerical example illustrating the application of the algorithm.

Abstract

The paper presents a novel iterative algorithm named Cₒ₀IA, which aims at finding common fixed points in CAT (0) space using quasi non-expansive mappings along with property (E). Also, we establish lemmas and theorems with the help of this algorithm and have demonstrated △-convergence to a common fixed point for two operators D and C in CAT (0) space. Furthermore, the paper includes a numerical example to support the main results.

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Common fixed point results via Cₒ₀IA using quasi non-expansive mappings in CAT (0) spaces

Key Points

Abstract

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