Search Results (14)

In 2003, W. Takahashi and M. Toyoda established the weak convergence of the iteration process of solving a variational inequality problem. This variational inequality is associated with an inverse strongly monotone mapping. In our recent research, we showed that most of the exact iterates of the same iterative process are approximate solutions of the variational inequality. In this paper, we apply a method with remote set control in order to find a common solution of a family of variational inequality problems, generated by inverse strongly monotone mappings, and a family of fixed point problems, which are not necessarily finite, in the presence of computational errors. Our results are obtained under the presence of summable and nonsummable computational errors. Full article

In vegetated coastal deltas, direct optical retrieval of surface soil salt content (SSC, 0–10 cm) is often hindered by canopy masking, mixed pixels, and seasonal variability in surface conditions. To improve SSC mapping under vegetation cover, this study developed a thresholded normalized difference vegetation index area-under-the-curve (NDVI-AUC) metric that integrates only the portion of the seasonal NDVI trajectory exceeding an ecologically defined threshold. Taking Dongying in the Yellow River Delta (YRD), China, as the study area, daily NDVI time series were reconstructed in Google Earth Engine (GEE) from Sentinel-2, Landsat-8/9, MODIS, and a Sentinel–Landsat fusion stream. An empirical electrical conductivity (EC)–SSC calibration was used to harmonize multi-year observations and construct a unified dataset of 177 topsoil samples collected in 2022, 2024, and 2025, which was divided into calibration (n = 118) and validation (n = 59) sets. Threshold traversal and Savitzky–Golay (SG) sensitivity tests were performed, and the negative exponential model was retained as the primary model after comparison with alternative monotonic decreasing functions. Across sensors, SSC showed a consistent inverse nonlinear relationship with NDVI-AUC. Threshold selection influenced model performance more strongly than SG smoothing. The Sentinel–Landsat fusion stream performed best, with R² values of 0.731 and 0.725 for calibration and validation, respectively, followed closely by Sentinel-2 (R² = 0.718 and 0.713). Landsat-8/9 showed moderate performance, whereas MODIS mainly represented background-scale patterns. The optimal 10 m implementation was further used to reconstruct annual SSC maps for 2021–2025, revealing stable coastal hotspots, localized bidirectional changes, and a modest model-derived decline in regional SSC. Overall, thresholded NDVI-AUC provides a simple, interpretable, and process-based metric for SSC mapping in vegetated coastal soils and can support agricultural decision makers in annual salinity hotspot screening and land management planning. Full article

In 2003 W. Takahashi and M. Toyodaestablished the weak convergence of an iteration process to solve a variational inequality problem induced by an inverse strongly-monotone mapping. Recently we proved that for the same iterative process, most of its exact iterates are approximate solutions of the variational inequality. It was also shown that the iteration process for solving a variational inequality problem for an inverse strongly-monotone mapping generates approximate solutions in the presence of computational errors. In this work we employ the Cimmino algorithm in order to generalize these results for common approximate solutions of a finite family of variational inequalities with inverse strongly-monotone mappings and of a finite family of fixed point problems in the presence of computational errors. Full article

This study proposes a new strongly convergent iterative framework obtained by combining a Krasnosel’skiǐ–Mann type subgradient extragradient process with a hybrid projection strategy and an inertial extrapolation mechanism. The method is applied to address hierarchical fixed-point problems (HFPPs) for nonexpansive and quasi-nonexpansive mappings as well as variational inequality problems (VIPs) involving a pseudomonotone operator in real Hilbert spaces. The proposed scheme employs step sizes that are restricted by the inverse of the Lipschitz constant of the underlying cost operator. Strong convergence of the iterates is achieved under mild hypotheses on the inertial parameter and control sequences. The method is further applied to problems arising in optimization and monotone operator theory. The results show that the proposed framework generalizes and integrates a number of existing approaches while offering improved computational performance. Full article

W. Takahashi and M. Toyoda (2003) proved weak convergence of an iteration process of solving a variational inequality problem for an inverse strongly-monotone mapping. In our recent work we showed that, for the same iterative process, most of its exact iterates are approximate solutions of the variational inequality. In this paper, we show that the iteration process for solving a variational inequality problem for an inverse strongly monotone mapping generates an approximate solution in the presence of small computational errors. We also estimate a number of iterates needed in order to obtain such an approximate solution. Full article

In 2003 W. Takahashi and M. Toyoda showed the weak convergence of an iteration process of finding the solution of a variational inequality problem for an inverse strongly monotone mapping. In the present paper, we show that for the same process, most of its iterates are approximate common solutions for a finite family of variational inequalities induced by inverse strongly monotone mappings. Full article

In this paper, we introduce a modified form of the G-variational inequality problem, called the combination of G-variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a G-nonexpansive mapping and the solution set of the proposed G-variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the G-minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the G-minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings. Full article

The main aim of this research is to introduce and investigate an inertial Tseng iterative method to approximate a common solution for the variational inequality problem for $\gamma$-inverse strongly monotone mapping and monotone inclusion problem in real Hilbert spaces. We establish a strong convergence theorem for our suggested iterative method to approximate a common solution for our proposed problems under some certain mild conditions. Furthermore, we deduce a consequence from the main convergence result. Finally, a numerical experiment is presented to demonstrate the effectiveness of the iterative method. The method and methodology described in this paper extend and unify previously published findings in this field. Full article

In this paper, we introduce a new numerical method for finding a common solution to variational inequality problems involving monotone mappings and null point problems involving a finite family of inverse-strongly monotone mappings. The method is inspired by the subgradient extragradient method and the regularization method. Strong convergence results of the proposed algorithms have been obtained under some suitable conditions. Full article

In this paper, we propose and study an iterative algorithm that comprises of a finite family of inverse strongly monotone mappings and a finite family of Lipschitz demicontractive mappings in an Hadamard space. We establish that the proposed algorithm converges strongly to a common solution of a finite family of variational inequality problems, which is also a common fixed point of the demicontractive mappings. Furthermore, we provide a numerical experiment to demonstrate the applicability of our results. Our results generalize some recent results in literature. Full article

In this paper, using a new shrinking projection method, we deal with the strong convergence for finding a common point of the sets of zero points of a maximal monotone mapping, common fixed points of a finite family of demimetric mappings and common zero points of a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we get well-known and new strong convergence theorems in a Hilbert space. Full article

We introduce an iterative algorithm which converges strongly to a common element of fixed point sets of nonexpansive mappings and sets of zeros of maximal monotone mappings. Our iterative method is quite general and includes a large number of iterative methods considered in recent literature as special cases. In particular, we apply our algorithm to solve a general system of variational inequalities, convex feasibility problem, zero point problem of inverse strongly monotone and maximal monotone mappings, split common null point problem, split feasibility problem, split monotone variational inclusion problem and split variational inequality problem. Under relaxed conditions on the parameters, we derive some algorithms and strong convergence results to solve these problems. Our results improve and generalize several known results in the recent literature. Full article

In this paper, based on the Yamada iteration, we propose an iteration algorithm to find a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping. We obtain a weak convergence theorem in Hilbert space. In particular, the set of zero points of an inverse strongly-monotone mapping can be transformed into the solution set of the variational inequality problem. Further, based on this result, we also obtain some new weak convergence theorems which are used to solve the equilibrium problem and the split feasibility problem. Full article

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem. Full article