Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces

Year : 2025 | Volume : 12 | Issue : 01 | Page : 1 05
    By

    pradip Kumar keer,

  • Geeta Agarwal,

  1. Research Scholar, Department of Mathematics, Government Motilal Vigyan Mahavidyalaya (Govt. MVM), Madhya Pradesh, India
  2. Professor, Department of Mathematics, Government Motilal Vigyan Mahavidyalaya (Govt. MVM), Madhya Pradesh, India

Abstract

This paper extends the Hicks contraction theory to multi-valued mappings within generalized b-Manger spaces, a class of metric-like structures that accommodate more flexible distance functions. By introducing new definitions, such as generalized admissibility conditions and weak compatibility in the multivalued sense, we provide a comprehensive analysis of how these contractions behave in broader topological and metric contexts. Our approach systematically generalizes classical contraction principles by relaxing conventional constraints, thereby broadening their applicability to non-standard frameworks. We establish a series of novel fixed-point theorems under various contractive-type conditions, such as graph-structured mappings, control functions, and altering distance functions, thereby capturing a more nuanced spectrum of convergence behaviour. These results not only subsume existing fixed-point theorems as special cases but also reveal deeper structural properties of the mappings involved, including orbital continuous and quasi-compact features. Examples are constructed to validate the theoretical framework, highlighting practical scenarios where our generalized theorems outperform classical counterparts. Furthermore, we investigate the stability, robustness, and iterative convergence of solution sets in the presence of perturbations, enhancing the understanding of solution behavior in applied settings. This work opens new avenues for future research in nonlinear analysis, particularly in extending fixed-point theory to hybrid metric spaces, fuzzy settings, and optimization in abstract systems.

Keywords: Hicks Contractions, Multi-Valued Mappings, Generalized b-Menger Spaces.

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article:
pradip Kumar keer, Geeta Agarwal. Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces. Research & Reviews: Discrete Mathematical Structures. 2025; 12(01):1-05.
How to cite this URL:
pradip Kumar keer, Geeta Agarwal. Expanding Hicks Contraction Theory, Multi-Valued Mappings in Generalized b-Menger Spaces. Research & Reviews: Discrete Mathematical Structures. 2025; 12(01):1-05. Available from: https://journals.stmjournals.com/rrdms/article=2025/view=207603


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Regular Issue Subscription Original Research
Volume 12
Issue 01
Received 02/03/2025
Accepted 05/03/2025
Published 15/04/2025
Publication Time 44 Days
144

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