A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.

In this paper, the authors use the idea of \(\beta _{F_{L}}\)-admissible mappings to prove some L-fuzzy fixed point theorems for a generalized contractive L-fuzzy mappings. Some examples and applications to L-fuzzy fixed points for L-fuzzy mappings in partially ordered metric spaces are also given, to support main findings.

Topological data analysis (TDA) methods have recently emerged as powerful tools for uncovering intricate patterns and relationships in complex biological data, demonstrating their effectiveness in identifying key genes in breast, lung, and blood cancer. In this study, we applied a TDA technique, specifically persistent homology (PH), to identify key pathways for early detection of hepatocellular carcinoma (HCC). Recognizing the limitations of current strategies for this purpose, we meticulously used PH to analyze RNA sequencing (RNA-seq) data from peripheral blood of both HCC patients and normal controls. This approach enabled us to gain nuanced insights by detecting significant differences between control and disease sample classes. By leveraging topological descriptors crucial for capturing subtle changes between these classes, our study identified 23 noteworthy pathways, including the apelin signaling pathway, the IL-17 signaling pathway, and the p53 signaling pathway. Subsequently, we performed a comparative analysis with a classical enrichment-based pathway analysis method which revealed both shared and unique findings. Notably, while the IL-17 signaling pathway was identified by both methods, the HCC-related apelin signaling and p53 signaling pathways emerged exclusively through our topological approach. In summary, our study underscores the potential of PH to complement traditional pathway analysis approaches, potentially providing additional knowledge for the development of innovative early detection strategies of HCC from blood samples.

The aim of this paper is to study some properties of both the coincidence point set and the set of common fixed points of two or more digitally continuous mappings. Moreover, we study how rigidity may affect the sets of coincidence and homotopy coincidence points. Additionally, we investigate if some well-established results in the Nielsen classical topology regarding the sets of coincidence for many maps remain valid in the digital topological setting.