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On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Author

Listed:
  • Qi Liu

    (School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
    These authors contributed equally to this work.)

  • Yongjin Li

    (School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
    These authors contributed equally to this work.)

Abstract

In this paper, we will introduce a new geometric constant L YJ ( λ , μ , X ) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and L YJ ( λ , μ , X ) . Also, this new coefficient is computed for X being concrete space.

Suggested Citation

  • Qi Liu & Yongjin Li, 2021. "On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces," Mathematics, MDPI, vol. 9(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:116-:d:476019
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