Some Fixed Point Results for Monotone Multivalued and Integral Type Contractive Mappings (European Journal of Pure and Applied Mathematics, 2025)
This study focuses on establishing fixed point results for monotone multivalued mappings within the framework of partially ordered complete $\mathfrak{D}^\star_b$-metric spaces. The partial order on the set $(\mathcal{W}, \preccurlyeq)$ is defined through a functional pair $(κ, Θ)$. The research further explores conditions under which coupled fixed points exist and are unique, particularly for mappings that meet certain contractive requirements. These investigations are carried out using the notion of integral-type contractions tailored to the structure of partially ordered $\mathfrak{D}^\star_b$-metric spaces. In addition to the core results, several corollaries are derived as specific instances. To enhance the reliability and relevance of the findings, the paper includes a number of illustrative examples.
Keywords: Metric space (MS); upper semi-continuous (USC); lower semi-continuous (LSC); fixed point (FP); partially ordered (PO); multivalued mapping (MM)