In the current manuscript, the notion of a cone -metric space over Banach’s algebra with parameter is introduced. Furthermore, using -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

中文翻译：

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Banach代数上锥度量空间上广义Hardy-Rogers压缩的不动点结果及其应用

在当前的手稿，圆锥体的概念-在巴拿赫的代数参数度量空间被引入。此外，使用-受理哈迪-罗杰斯的压缩条件，我们已经证明固定点定理自映射，推广和加强许多现有文献的结论。为了验证我们的关键结果，给出了一个非平凡的例子，并且作为一个应用，我们证明了一个定理，该定理表明了一个无限积分方程组的解的存在。