This article demonstrates the graphical existence of a single fixed point while imposing the contractive condition of Chatterjea type -contraction on -metric space (briefly as -MS). We present two examples that verify the validity of the results given in the paper. The paper further explains the subsistence of the fixed point even if the contractive condition is valid only for a closed ball inside the space rather than imposing it on the whole -MS. Moreover, the application of the mentioned results in finding a single solution of functional equations is described that is widely used in computer programming and optimization.

中文翻译：

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功能方程的3D动态编程方法及其应用

本文演示单个固定点的图形存在，而强加Chatterjea类型的收缩条件-收缩上-度量空间（简略- MS）。我们提供了两个示例来验证本文给出的结果的有效性。论文进一步解释了固定点的存在性，即使收缩条件仅对空间内部的闭合球有效，而不是将其强加于整个空间（ MS）。此外，描述了上述结果在寻找函数方程的单个解中的应用，该函数被广泛用于计算机编程和优化中。