An algorithm is introduced to find an answer to both inclusion problems and fixed point problems. This algorithm is a modification of Tseng type methods inspired by Mann’s type iteration and viscosity approximation methods. On certain conditions, the iteration obtained from the algorithm converges strongly. Moreover, applications to the convex feasibility problem and the signal recovery in compressed sensing are considered. Especially, some numerical experiments of the algorithm are demonstrated. These results are compared to those of the previous algorithm.

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

In this paper, we introduce a new concept of dominating proximal generalized Geraghty for two mappings and prove the existence and uniqueness of a common best proximity coincidence point in complete metric spaces. And also, we give an example for the main theorems. The main theorem is a generalization and improvement of some well-known theorems.

In this paper, we initiate a concept of graph-proximal functions. Furthermore, we give a notion of being generalized Geraghty dominating for a pair of mappings. This permits us to establish the existence of and unique results for a common best proximity point of complete metric space. Additionally, we give a concrete example and corollaries related to the main theorem. In particular, we apply our main results to the case of metric spaces equipped with a reflexive binary relation. Finally, we demonstrate the existence of a solution to boundary value problems of particular second-order differential equations.

Northern Thailand frequently suffers from severe PM2.5 air pollution, especially during the dry season, due to agricultural burning, local emissions, and transboundary haze. Understanding how pollution moves across regions and identifying source–receptor relationships are critical for effective air quality management. This study investigated the spatial and temporal dynamics of PM2.5 in northern Thailand. Specifically, it explored how pollution at one monitoring station influenced concentrations at others and revealed the seasonal structure of PM2.5 transmission using network-based analysis. We developed a Python-based framework to analyze daily PM2.5 data from 2022 to 2023, selecting nine representative stations across eight provinces based on spatial clustering and shape-based criteria. Delaunay triangulation was used to define spatial connections among stations, capturing the region’s irregular geography. Cross-correlation and Granger causality were applied to identify time-lagged relationships between stations for each season. Trophic coherence analysis was used to evaluate the hierarchical structure and seasonal stability of the resulting networks. The analysis revealed seasonal patterns of PM2.5 transmission, with certain stations, particularly in Chiang Mai and Lampang, consistently acting as source nodes. Provinces such as Phayao and Phrae were frequently identified as receptors, especially during the winter and rainy seasons. Trophic coherence varied by season, with the winter network showing the highest coherence, indicating a more hierarchical but less stable structure. The rainy season exhibited the lowest coherence, reflecting greater structural stability. PM2.5 spreads through structured, seasonal pathways in northern Thailand. Network patterns vary significantly across seasons, highlighting the need for adaptive air quality strategies. This framework can help identify influential monitoring stations for early warning and support more targeted, season-specific air quality management strategies in northern Thailand.

In this work, an algorithm is introduced for the problem of finding a common fixed point of a finite family of G-nonexpansive mappings in a real Hilbert space endowed with a directed graph G. This algorithm is a modified parallel algorithm inspired by the inertial method and the Mann iteration process. Moreover, both weak and strong convergence theorems are provided for the algorithm. Furthermore, an application of the algorithm to a signal recovery problem with multiple blurring filters is presented. Consequently, the numerical experiment shows better results compared with the previous algorithm.