Orthogonality of $\mathfrak{p}$-angular distance in relation to double-parametric integrals

Authors

  • Jinyu Xia School of Mathematical Sciences, Chengdu University of Technology, Chengdu, China
  • Qi Liu School of Mathematics and Statistics, Anqing Normal University, Anqing, China
  • Yuxin Wang School of Mathematics and Statistics, Anqing Normal University, Anqing, China
  • Man Liang School of Mathematics and Statistics, Anqing Normal University, Anqing, China
  • Silvestru Sever Dragomir Applied Mathematics Research Group, ISILC, Victoria University, Melbourne, Australia

DOI:

https://doi.org/10.3842/umzh.v78i9-10.9561

Keywords:

Integral orthogonality, $\mathfrak{p}$-angular, existence, inner product space

Abstract

UDC 517.98

We put forward a new concept of integral orthogonality with two parameters by combining the $\mathfrak{p}$-angular distance and Hermite–Hadamard integral orthogonality within real normed spaces. Our intention is to characterize inner product spaces and investigate the principal properties of this type of orthogonality. We have demonstrated its existence by using the Intermediate Value Theorem. Furthermore, by using the Gâteaux differentiability of the norm, we provide a characterization of the inner product space.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 9-10, 2026.

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Published

19.09.2026

Issue

Vol. 78 No. 9-10 (2026)

Section

Research articles