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Complex convexity and fixed point theorems in Orlicz modular spaces

Tom 119 / 2019

Lili Chen, Deyun Chen, Yang Jiang Banach Center Publications 119 (2019), 47-56 MSC: Primary 46B20; Secondary 46E30. DOI: 10.4064/bc119-3

Streszczenie

In this paper, we prove that every Orlicz modular function space $L_{\Phi ,\rho }$ is complex midpoint locally uniformly convex. As a corollary, $L_{\Phi ,\rho }$ is also complex strictly convex. Furthermore, we introduce the notions of mean nonexpansive mappings in the modular sense and prove a fixed point theorem in Orlicz modular function spaces.

Autorzy

  • Lili ChenCollege of Mathematics and Systems Science
    Shandong University of Science and Technology
    Qingdao 266590, China
    and
    Department of Mathematics
    Harbin University of Science and Technology
    Harbin 150080, China
    e-mail
  • Deyun ChenCollege of Computer Science and Technology
    Harbin University of Science and Technology
    Harbin 150080, China
    e-mail
  • Yang JiangDepartment of Mathematics
    Harbin University of Science and Technology
    Harbin 150080, China
    e-mail

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