Analysis of Fixed Points in Complex G-Metric Frameworks: Theoretical Foundations and Applications

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DOI: https://doi.org/10.28924/2291-8639-24-2026-153
Published: May 20, 2026
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Elhadi Dalam, Analysis of Fixed Points in Complex G-Metric Frameworks: Theoretical Foundations and Applications, Int. J. Anal. Appl., 24 (2026), 153.

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Elhadi Dalam

Abstract

Introducing new theoretical conclusions that integrate and expand existing concepts from complex-valued metric, b-metric, and G-metric spaces, this research provides a full extension of fixed point theory to the framework of complex G-metric (cG-m) spaces. This extension is presented in this paper. Through the process of redefining the concept of distance in contexts that involve complicated values, the study creates a solid analytical framework for the purpose of analyzing mappings that are regulated by complex contraction conditions. In this study, novel Banach-type and rational contractive mappings are constructed and investigated, which ultimately leads to the formulation of existence and uniqueness theorems for fixed points under generalized contractive inequalities. Both of these ideas are discussed in the research that was conducted. These discoveries not only increase the breadth of the results of conventional research, but they also bring to light the complete application of fixed point theory to a wider range of problems. This is a significant contribution to the field of psychology. Nonlinear dynamic models, complex systems, and integral equations are all things that fall under this category of difficulties. Through the provision of a unified and extendable framework for fixed point solutions in complex-valued metric spaces, the research offers a contribution to the progress of the theoretical landscape of nonlinear analysis. This is accomplished by offering a framework that is both unified and extensible. Furthermore, it sets the framework for future work in computational and applied mathematics, which is a significant contribution.

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