July 5, 2025

Convexity Theorem for Hyperbolic Functions in Complex Analysis

Puntos clave

Necessary conditions for convexity are identified in differentiable functions of hyperbolic numbers, indicating a new direction for research in complex analysis.
The study builds on the zero-divisor factorization theorem to establish convexity conditions, enhancing understanding of hyperbolic functions.
Research employs properties of hyperbolic numbers, a mathematical structure with unique characteristics, to derive results on convexity.
These findings may bridge concepts from real analysis to hyperbolic complex analysis, underscoring the relevance of hyperbolic functions in various applications.

Resumen

This paper studies the convexity of hyperbolic complex functions, where hyperbolic numbers are commutative rings that contain zero divisors and are composed of two real numbers. Based on the zero-divisor factorization theorem of hyperbolic numbers and other properties of functions of hyperbolic numbers, this article establishes necessary and sufficient conditions for the convexity of -differentiable functions with hyperbolic complex variables. This study, which generalizes the convexity characterization theorems from real analysis to the hyperbolic complex plane, will further establish a theoretical research foundation for the function theory of hyperbolic complex analysis and meanwhile provide impetus for the application of hyperbolic functions in physics.

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Cite This Study

Feng et al. (Sat,) studied this question.

synapsesocial.com/papers/68af521fad7bf08b1ead9d2f https://doi.org/https://doi.org/10.54097/5yfz3q63

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