This manuscript established the concept of $b$-Ciric $\mathtt{\pounds }$-fuzzy soft contractions (BCLFSC) within $b$-metric spaces, presenting a framework to analyze fixed points of $\mathtt{\pounds }$-fuzzy soft set-valued mappings under these conditions. Leveraging lattice-valued memberships, our framework enables more sophisticated decision-making processes, providing flexibility to structure criteria and relationships hierarchically. An illustrative example was provided to support the theoretical foundations, demonstrating the use of $\mathtt{\pounds }$-fuzzy soft sets in decision-making contexts where nuanced, multi-attribute evaluations are essential. Additionally, our approach was applied to fractional integral equations, showcasing how these results unify and expand current methodologies in both conventional and non-classical fixed point theory. This study built on the foundational work in $b$-metric spaces by incorporating recent advances in fuzzy and soft set theory, particularly within complex decision-making and fractional essential inclusion applications. While our model accommodates intricate, ambiguous datasets, which is advantageous in multi-criteria assessments, we acknowledge computational demands as a limitation. This paper concludes with a discussion of implications for future research, underscoring the potential for further development in lattice-valued decision frameworks and applications to new domains.

A modified Halpern-type iterative technique, having weak and strong convergence results for approximating invariant points of a new class of enriched nonspreading operators subject to some standard mild conditions in the setting of real Banach spaces, was presented in this work. It was demonstrated with an example that the class of enriched nonspreading mappings includes the class of nonspreading mappings. Again, it was demonstrated with nontrivial examples that the class of enriched nonspreading mappings and the class of enriched nonexpansive mappings are independent. Some basic properties of the class of enriched nonspreading mappings were established. The results obtained solve the open question raised in Nonlinear Analysis 73 (2010): 1562–1568 for nonspreading-type mappings incorporating an averaged mapping. Moreover, we studied the estimation of common invariant points of this new class of mappings and the class of enriched nonexpansive operators and provided a strong convergence theorem for these mappings.