Existence Theory for Positive Iterative Solutions to a Type of Boundary Value Problem

We introduce some research results on a type of third-order boundary value problem for positive iterative solutions. The existence of solutions to these problems was proved using the monotone iterative technique. As an examination of the proposed method, an example to illustrate the effectiveness of our results was presented.

Iterative Solutions for the Differential Equation with p -Laplacian on Infinite Interval

This paper systematically investigates a class of fourth-order differential equation with p -Laplacian on infinite interval in Banach space. By means of the monotone iterative technique, we establish not only the existence of positive solutions but also iterative schemes under the suitable conditions. At last, we give an example to demonstrate the application of the main result.

Corrections to: Efficient iterative solutions to complex-valued nonlinear least-squares problems with mixed linear and antilinear operators

A correction to this paper has been published: https://doi.org/10.1007/s11081-021-09631-1

Stacked Community Prediction: A Distributed Stacking-Based Community Extraction Methodology for Large Scale Social Networks

Nowadays, due to the extensive use of information networks in a broad range of fields, e.g., bio-informatics, sociology, digital marketing, computer science, etc., graph theory applications have attracted significant scientific interest. Due to its apparent abstraction, community detection has become one of the most thoroughly studied graph partitioning problems. However, the existing algorithms principally propose iterative solutions of high polynomial order that repetitively require exhaustive analysis. These methods can undoubtedly be considered resource-wise overdemanding, unscalable, and inapplicable in big data graphs, such as today’s social networks. In this article, a novel, near-linear, and highly scalable community prediction methodology is introduced. Specifically, using a distributed, stacking-based model, which is built on plain network topology characteristics of bootstrap sampled subgraphs, the underlined community hierarchy of any given social network is efficiently extracted in spite of its size and density. The effectiveness of the proposed methodology has diligently been examined on numerous real-life social networks and proven superior to various similar approaches in terms of performance, stability, and accuracy.

Iterative Solutions for Solving Variational Inequalities and Fixed-Point Problems

In this paper, we are interested in variational inequalities and fixed-point problems in Hilbert spaces. We present an iterative algorithm for finding a solution of the studied variational inequalities and fixed-point problems. We show the strong convergence of the suggested algorithm.

Monotone iterative solutions for a coupled system of p-Laplacian differential equations involving the Riemann–Liouville fractional derivative

Applying the monotone iterative technique and the method of upper and lower solutions, we investigate the existence of extremal solutions for a nonlinear system of p-Laplacian differential equations with nonlocal coupled integral boundary conditions. We present a numerical example to illustrate the main result.