Dugundgji’s Extension Theorem and Fixed Point Theorem in <em>p</em>-normed Spaces

The goal of this paper is to establish Dugundji&rsquo;s extension theorem in p-normed spaces, and then as applications, fixed theorems in p-normed spaces are given for p &isin; (0, 1]. The results in this paper would provide a general fundamental basis for the development of fixed point theory, in supporting for the study of Schauder&rsquo;s conjecture and related nonlinear analysis in p-vector spaces which are either finite or infinite-dimensional. In particularly, how important the Dugundgji type extension and fixed-point theorem in p-normed spaces can be found from Yuan&rsquo;s recent work in [41]-[42] and related discussion wherein.