Fixed Point Theorems for Rus-Hicks-Rhoades Contractive Mappings in Orthogonal Quasi-Metric Spaces With Applications to Orthogonal System Models
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Date
2025-09-29
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Taylor & Francis
Abstract
In this study, we explore fixed point theorems for Rus-Hicks-Rhoades-Jaggi hybrid combinational type mappings within orthogonal quasi-metric spaces. To illustrate and validate these results, an example is provided. Additionally, we highlight a practical application by connecting the theoretical findings to an orthogonal model in commu nication theory. Specifically, we relate the results to space-time block coding (STBC) in multiple-input multiple-output (MIMO) systems, where the fixed point solution repre sents the equilibrium state of iterative decoding, ensuring convergence to a stable codeword reconstruction even in the presence of channel disturbances. Moreover, we show that the Helmholtz equation with mixed boundary conditions possesses a unique f ixed point. This framework has broad applicability: in acoustics, it models vibrations in air columns of closed-open tubes; in electromagnetic, it describes field distributions in wave-guides and resonant cavities; and in mechanics, it represents vibrations of beams with one fixed and one free end. Such formulations demonstrate how Helmholtz phenomena under mixed boundary value problems provide insights into wave propa gation, resonance control, and system stability, thereby enriching both the theoretical understanding of fixed-point analysis and its engineering applications.
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This journal article was published by Taylor & Francis in 2025