The Extended Cone b_2-Metric-like Spaces on Banach Algebra and Their Applications
Keywords:
Fixed point, Extended b_2-metric space, Extended cone b-metric-like space, Generalized Lipschitz mappings.Abstract
In this paper, we initiate a groundbreaking investigation into the field of metric spaces by presenting the idea of an extended cone -metric-like space within the context of Banach algebra., aiming to bridge and extend their properties. Within the framework of this newly defined space, we formulate multiple fixed point theorems., providing a foundation for further analytical investigations. To demonstrate the practical utility and applicability of our theoretical findings, we present an application to Fredholm integral equation, showcasing how the developed fixed-point results can be employed to solve real-world problems. Notably, our results contribute to the broader landscape of fixed-point theory and serve to generalize certain previously established results by Fernandez, J., et al., released in 2017 and 2022, thus advancing the field and offering more comprehensive tools for analysis.
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