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Utami, Yulia
STMIK Pelita Nusantara Medan
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Journal : International Journal of Basic and Applied Science

 1 
Fixed Point Theory in Generalized Metric Vector Spaces and their applications in Machine Learning and Optimization Algorithms Vinsensia, Desi; Utami, Yulia
International Journal of Basic and Applied Science Vol. 13 No. 2 (2024): Sep: Basic and Applied Science
Publisher : Institute of Computer Science (IOCS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35335/ijobas.v13i2.504

Abstract

This study introduces a novel formulation of fixed-point theory within Generalized metric spaces, with an emphasis on applications in machine learning optimization and high-dimensional data analysis. Recall on the concept of complete G-metric spaces, we define a generalized contraction condition tailored for operators representing iterative updates in machine learning algorithms. The proposed framework is exemplified through gradient descent with regularization, demonstrating convergence within a non-Euclidean, high-dimensional setting. Results reveal that our approach not only strengthens convergence properties in iterative algorithms but also complements modern regularization techniques, supporting sparsity and robustness in high-dimensional spaces. These findings underscore the relevance of G-metric spaces and auxiliary functions within fixed-point theory, highlighting their potential to advance adaptive optimization methods. Future work will explore further applications across machine learning paradigms, addressing challenges such as sparse data representation and scalability in complex data environments.
Advancing optimization algorithms with fixed point theory in generalized metric vector spaces Vinsensia, Desi; Utami, Yulia; Awawdeh, Benavides Khan; Bausch, Nocedals Bertesh
International Journal of Basic and Applied Science Vol. 13 No. 3 (2024): Dec: Optimization and Artificial Intelligence
Publisher : Institute of Computer Science (IOCS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35335/ijobas.v13i3.621

Abstract

This research develops and evaluates an adaptive parameter-based fixed point iterative algorithm within generalized metric vector spaces to improve stability and convergence speed in optimization problems. The study extends fixed point theory beyond classical metric spaces by incorporating a more flexible structure that accommodates non-Euclidean systems, commonly found in machine learning, data analysis, and dynamic systems optimization. The proposed adaptive fixed point algorithm modifies the conventional iterative method: where the adaptive parameter dynamically adjusts based on the previous iterations: with as a control constant. A numerical case study demonstrates the algorithm’s effectiveness, comparing it with the classical Banach Fixed Point Theorem. Results show that the adaptive method requires fewer iterations to achieve convergence while maintaining higher stability, significantly outperforming the standard approach. The findings suggest that incorporating adaptive parameters in fixed point iterations enhances computational efficiency, particularly in non-convex optimization and deep learning training models. Future research will explore the algorithm’s robustness in high-dimensional spaces, its integration with hybrid optimization techniques, and applications in uncertain and noisy environments.
The completeness role of the function ϕ in generating the Riesz potential operator Vinsensia, Desi; Utami, Yulia; Addini, Puteri Fadjar
International Journal of Basic and Applied Science Vol. 13 No. 4 (2025): Computer Science, Engineering, Basic and Applied mathematics Science
Publisher : Institute of Computer Science (IOCS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35335/ijobas.v13i4.637

Abstract

The Riesz potential operator is a central tool in harmonic analysis and the theory of partial differential equations, commonly defined via convolution with a singular Kernel. In many modern frameworks, function space are generated by a mappings involving such operators. In this paper, we explore the dual role of the generating function- in: (i). Defining the Riesz function space and (ii). Ensuring its completeness. We introduce a Riesz function space whose norm is induced growth function- (a Young function). We establish, through several examples and proofs, that under suitable conditions (specifically, the condition on ), the space is complete. Furthemore, we illustrate discrete analogues and applications to Orlicz space, thereby underscoring the fundamental importance of in both the construction and Banach space structure of these function spaces.
Co-Authors Abdul Rahman Hakim Abdul Rahman Hakim Addini, Puteri Fadjar Adelia Febriana Amala, Dwi Novia Angga Ramadhan Annas Prasetio Arya Riski Tarigan Aura Nissa Awaluddin Fitra Awawdeh, Benavides Khan Bausch, Nocedals Bertesh Bosker Sinaga Chairullah, Andry Devie Indah Wulandari Erwin Pangabean Erwin Panggabean Fitra, Awaludin Fitra, Awaludin Gulo, Dwiki Fodes Nosara Handayani, Sri Husaini, Adam Ida Ayu Putu Sri Widnyani Jannah, Nadiyatul Kartika Lubis, Risa Khairul Azmi Khairunnisa Khairunnisa Khairunnisa Kumala Dewi, Intan Kumala, Winda Lubis, Risa Kartika Martua Sitorus Martua Sitorus Mestriawan Barasa Mian Sari Simanjuntak Muhamad Alda Muhammad Arifin Nandiyantul Jannah Nurul Istiqomah Prasetio, Annas Pria Muslim pria muslim harahap Pria Muslim Rasmana Purba, Elisa Purba, Elisa Rahmawida, Joya Ravindran Rina Nanda Hanifa Risa Kartika Lubis Senjaya, Chessie Paquita Sianturi, Ariani Natalia Siregar, Fathia Sitompul, Kristin Lourensi Situmorang, Junita Sulastri Sulastri Sulastri SURYANI Susi Susanti Tumangger, Oktavia Vinsensia, Desi Zarina, Siti