In this paper, we propose a definition for a semi-inner product in the space of p-summable sequences equipped with an n-norm. Using this definition, we introduce the concepts of pn-orthogonality and the pn-angle between two vectors in the space of p-summable sequences. For the special case n = 1, these concepts are identical to previous studies. We also introduce the notion of the pn-angle between one-dimensional subspaces and arbitrary-dimensional subspaces. The authors believe that the results obtained in this paper are very significant, especially in the theory of n-normed space in functional analysis.

More from our Archive

• DOI: 10.3390/sym15071324 2023

  The Analysis of Bifurcation, Quasi-Periodic and Solitons Patterns to the New Form of the Generalized q-Deformed Sinh-Gordon Equation

  Syeda Sarwat Kazmi, Adil Jhangeer, Nauman Raza, Haifa I. Alrebdi, Abdel-Haleem Abdel-Aty, Hichem Eleuch

• DOI: 10.3390/math11143069 2023

  An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil

  Raydonal Ospina, João A. M. Gondim, Víctor Leiva, Cecilia Castro

• DOI: 10.1098/rsta.2022.0217 2023

  Analysing the dynamic structure of warm dense matter in the imaginary-time domain: theoretical models and simulations

  Tobias Dornheim, Jan Vorberger, Zhandos A. Moldabekov, Maximilian Böhme

• DOI: 10.3390/math11143133 2023

  Dynamic RNA Coding Color Image Cipher Based on Chain Feedback Structure

  Heping Wen, Shenghao Kang, Zhuxi Wu, Yiting Lin, Yiming Huang

• DOI: 10.3390/math11143110 2023

  Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures

  Zhifu Jia, Cunlin Li

• DOI: 10.3390/math11143052 2023

  Greenhouse Micro-Climate Prediction Based on Fixed Sensor Placements: A Machine Learning Approach

  Oladayo S. Ajani, Member Joy Usigbe, Esther Aboyeji, Daniel Dooyum Uyeh, Yushin Ha, Tusan Park, Rammohan Mallipeddi

• DOI: 10.3390/math11133022 2023

  Mathematical Modelling of Fused Deposition Modeling (FDM) 3D Printing of Poly Vinyl Alcohol Parts through Statistical Design of Experiments Approach

  Mahmoud Moradi, Mojtaba Karamimoghadam, Saleh Meiabadi, Giuseppe Casalino, Mohammad Ghaleeh, Bobymon Baby, Harikrishna Ganapathi, Jomal Jose, Muhammed Shahzad Abdulla, Paul Tallon, Mahmoud Shamsborhan, Mohammad Rezayat, Satyam Paul, Davood Khodadad

• DOI: 10.3390/math11133008 2023

  Prognostics and Health Management of Rotating Machinery of Industrial Robot with Deep Learning Applications—A Review

  Prashant Kumar, Salman Khalid, Heung Kim

• DOI: 10.3390/sym15071338 2023

  Nonlinear Dynamics of a Piecewise Modified ABC Fractional-Order Leukemia Model with Symmetric Numerical Simulations

  Hasib Khan, Jehad Alzabut, Wafa F. Alfwzan, Haseena Gulzar

• DOI: 10.1002/mma.9474 2023

  Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type

  Nabil Chems Eddine, Phuong Duc Nguyen, Maria Alessandra Ragusa