Stability Framework for Quintuple Fixed Point of Mixed Monotone Operators with Contractive Conditions in Cauchy Spaces
DOI:
https://doi.org/10.63746/njtd.v22i4.3694Keywords:
Quintuple fixed points, Mixed monotone operators, Stability analysis, Contractive conditions, Cauchy spacesAbstract
The stability of quintuple fixed point for mixed monotone operators in partially ordered metric spaces remains underexplored, especially under generalised contractive conditions in Cauchy spaces. This study addresses this theoretical gap by developing a novel iterative procedure for quintuple fixed point. The methodology introduces a generalised contractive type mapping and uses recursive inequalities alongside matrix-based comparison techniques to establish convergence and stability criteria. These analytical tools are adapted to vector-valued sequences, enabling precise control over componentwise convergence behaviour. A new iteration framework is defined and rigorously analysed within a complete Cauchy-type metric space. The results reveal that the scheme ensures both the existence and stability of the fixed point. An illustrative real-valued application validates the theoretical framework. This approach unifies and extends previous work on coupled, tripled, and quadrupled fixed point, offering a robust analytical foundation for high-dimensional operator systems and future applications in nonlinear, fractional, or fuzzy dynamical models.
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