Abstract

A new class of mappings, called relatively continuous, is introduced and incorporated to elicit best proximity pair theorems for a non-self-mapping in the setting of reflexive Banach space. As a consequence we obtain a generalization of Carathéodory extension theorem for an initial value problem with L ¹ functions on the right hand side.

中文翻译：

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最佳邻近对的存在和Carathéodory定理的推广

摘要

引入并合并了一类称为相对连续的新型映射，以在自反Banach空间的设置中为非自映射得出最佳接近对定理。结果，我们获得了在右手边具有L ¹函数的初值问题的Carathéodory扩展定理的推广。