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Cayley-Dickson algebra-valued metric spaces and convergent fixed point theory for hypercomplex contractions | ||
| Journal of Hyperstructures | ||
| دوره 15، شماره 1، شهریور 2026، صفحه 123-137 اصل مقاله (1.65 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.18293.1134 | ||
| نویسندگان | ||
| Meghlal Mallik* 1؛ Abhijit Mandal2 | ||
| 1Department of Mathematics, Raiganj Surendranath Mahavidyalaya | ||
| 22Department of Mathematics, Raiganj Surendranath Mahavidyalaya, West Bengal, India | ||
| چکیده | ||
| This paper introduces a novel theoretical framework for metric spaces valued in Cayley-Dickson algebras, extending beyond the limitations of bicomplex-valued b metric spaces to encompass the entire hierarchy of hypercomplex number systems in cluding quaternions, octonions, and sedenions. We establish a comprehensive theory of Cayley-Dickson algebra-valued metric spaces (CD-metric spaces) with generalized triangle inequalities parameterized by coefficients that account for the non-associative and non-commutative properties inherent in higher-dimensional Cayley-Dickson con structions. Our principal contributions include: (1) the formulation of a consistent partial ordering relation across all finite-dimensional Cayley-Dickson algebras, (2) the development of convergence theory and completeness criteria for CD-metric spaces, (3) the establishment of fixed point theorems for contractive mappings under rational type conditions involving hypercomplex control functions, and (4) novel applications to systems of hypercomplex integral equations. The results significantly generalize existing bicomplex metric space theory and provide new tools for analyzing fixed point problems in non-associative algebraic structures. | ||
| کلیدواژهها | ||
| hypercomplex metric spaces؛ fixed point theory؛ non-associative analysis؛ octonions؛ sedenions؛ contractive mappings؛ integral equations | ||
| مراجع | ||
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