Existence of Fixed Points of Nonexpansive Mappings in Uniformly n-Convex n-Banach Spaces

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@article{1723338,
      author = {Anyande Benard Alex, Patrick Makila Wanjala},
      title = {Existence of Fixed Points of Nonexpansive Mappings in Uniformly n-Convex n-Banach Spaces},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {10},
      number = {3},
      pages = {2494-2497},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1723338.pdf},
      abstract = {This paper establishes the existence of fixed points of nonexpansive mappings on bounded closed convex subsets of uniformly n-convex n-Banach spaces. Building on the geometric properties of such spaces—reflexivity, weak compactness of bounded closed convex sets, and n-normal structure—we first prove an n-demi-closedness principle: for a nonexpansive self-map T, the mapping I-T is demi-closed at zero. Using this principle together with an approximate fixed point sequence generated by a family of n-normed contractions, we prove an n-normed analogue of the Browder–Göhde–Kirk theorem, namely that every nonexpansive self-map of a nonempty bounded closed convex subset of a uniformly n-convex n-Banach space has a fixed point. We further show that the fixed point set is closed and convex, and we establish a fixed point theorem valid in any reflexive n-Banach space with n-normal structure, obtained through a minimal-invariant-set argument of Kirk type. The results extend the classical fixed point theory of nonexpansive mappings, and the case n=2, to all n≥2.},
      keywords = {Approximate fixed point sequence, Demi-closedness, Fixed point property, Nonexpansive mapping, n-Normal structure.},
      month = {September},
  }