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<p>In the present paper, we introduce and analyze the concept of linear degree of nondensifiability (<i>L</i>-DND) in Banach spaces. For this, we will use the so-called degree of nondensifiability (DND), which is closely related with the Hahn-Mazurkiewicz theorem, and a suitable class of operators (linear and bounded) in the given Banach space. Although this extension of the DND inherits the same basic properties as the DND, examples show cases where the <i>L</i>-DND improves the applications of the DND. In particular, this new concept provides us an alternative to an already proved fixed point result based on the DND. As an application, we prove under suitable conditions an existence result for certain Volterra integral equations posed in the Banach space of all continuous functions from [0,&#xa0;1] into a Banach space.</p>

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THE LINEAR DEGREE OF NONDENSIFIABILITY IN BANACH SPACES AND APPLICATIONS

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • G. García

摘要

In the present paper, we introduce and analyze the concept of linear degree of nondensifiability (L-DND) in Banach spaces. For this, we will use the so-called degree of nondensifiability (DND), which is closely related with the Hahn-Mazurkiewicz theorem, and a suitable class of operators (linear and bounded) in the given Banach space. Although this extension of the DND inherits the same basic properties as the DND, examples show cases where the L-DND improves the applications of the DND. In particular, this new concept provides us an alternative to an already proved fixed point result based on the DND. As an application, we prove under suitable conditions an existence result for certain Volterra integral equations posed in the Banach space of all continuous functions from [0, 1] into a Banach space.