ITERATION SCHEME FOR TWO NONLINEAR MAPPINGS IN CAT(0) SPACES

Abstract

This paper develops an explicit two step iteration scheme for a coupled pair of nonlinear mappings in CAT(0) spaces. The framework treats a single-valued asymptotically nonexpansive mapping t and a multivalued asymptotically nonexpansive mapping T thatare coupled through a nonexpansive mapping. Under standard bounded control parameters and a summable asymptotic modulus, we prove Δ-convergence of the generated sequence toa common fixed point of t and T. The analysis exploits the intrinsic nonpositive curvature of CAT(0) spaces via quasi-Fejér estimates and a demiclosedness principle for (asymptotically)nonexpansive mappings, while the metric selection provides a stable interface between the single and multivalued components. The resulting theory yields a geometry-aware and computationally transparent algorithmic template for hybrid fixed point problems, with model examples illustrating scope and applicability.