Th. M. Rassias

Numerical solutions of third-order obstacle problems

It is known that a class of odd order obstacle problems in physical oceanography can be studied in the framework of variational inequality theory. In this paper, we show that variational inequalities related with third-order obstacle problems can be characterized by a system of variational equations without constraints, which are solved using modified finite difference technique. A comparison between our and other available results is also presented.

Inertial projection and contraction algorithms for variational inequalities

In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.

Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings

In this article, we first introduce a modified inertial Mann algorithm and an inertial CQ-algorithm by combining the accelerated Mann algorithm and the CQ-algorithm with the inertial extrapolation, respectively. This strategy is intended to speed up the convergence of the given algorithms. Then we established the convergence theorems for two provided algorithms. For the inertial CQ-algorithm, the conditions on the inertial parameters are very weak. Finally, the numerical experiments are presented to illustrate that the modified inertial Mann algorithm and inertial CQ-algorithm may have a number of advantages over other methods in computing for some cases.

Functional Inequalities Associated with Cauchy Additive Functional Equation in Non-Archimedean Spaces

We investigate the generalized Hyers-Ulam stability of the functional inequalities and in non-Archimedean normed spaces in the spirit of the Th. M. Rassias stability approach.

General Cubic-Quartic Functional Equation

We obtain the general solution and the generalized Hyers-Ulam stability of the general cubic-quartic functional equation for fixed integers k with 𝑘≠0,±1: 𝑓(𝑥

“Optimal” choice of the step length of the projection and contraction methods for solving the split feasibility problem

In this paper, first, we review the projection and contraction methods for solving the split feasibility problem (SFP), and then by using the inverse strongly monotone property of the underlying operator of the SFP, we improve the “optimal” step length to provide the modified projection and contraction methods. Also, we consider the corresponding relaxed variants for the modified projection and contraction methods, where the two closed convex sets are both level sets of convex functions. Some convergence theorems of the proposed methods are established under suitable conditions. Finally, we give some numerical examples to illustrate that the modified projection and contraction methods have an advantage over other methods, and improve greatly the projection and contraction methods.