巴拿赫空间中的φ-最佳邻近点与邻近型算法
On $ϕ$-Best Proximity Points and Proximal-type Algorithms in Banach Spaces
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中文总结 AI 辅助
本文研究巴拿赫空间中φ-最佳邻近点的存在与收敛性，提出收缩投影算法及投影方案，为求解含非自映射的非线性问题提供新工具。
中文摘要 AI 辅助
本文旨在研究巴拿赫空间中φ-最佳邻近点的存在性与收敛性。通过采用收缩投影算法，建立了强收敛定理，该算法用于计算邻近弱抑制映射的公共φ-最佳邻近点。最后，提出了一种投影方案，以求解巴拿赫空间中的分裂φ-最佳邻近点与变分问题。这些贡献为求解涉及非自映射的非线性问题提供了新工具。
英文摘要
The purpose of this paper is to study the existence and convergence of $ϕ$-best proximity points in Banach spaces. A strong convergence theorem is established by employing a shrinking projection algorithm designed to compute common $ϕ$-best proximity points of a proximally weakly suppressive mapping. Finally, we address a projection scheme to solve split $ϕ$-best proximity point and variational problem in a Banach space. These contributions provide new tools for solving nonlinear problems involving non-self mappings.
