An Improved Alternating CQ Algorithm for Solving Split Equality Problems

The CQ algorithm is widely used in the scientific field and has a significant impact on phase retrieval, medical image reconstruction, signal processing, etc. Moudafi proposed an alternating CQ algorithm to solve the split equality problem, but he only obtained the result of weak convergence. The work of this paper is to improve his algorithm so that the generated iterative sequence can converge strongly.

The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems

In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with random impulses. Then, we get the equivalent integral equation of the random impulsive differential equation. Based on this integral equation, we use Dhage’s fixed point theorem to prove the existence of solutions to the equation, and the theorem is extended to the general second order nonlinear random impulsive differential equations. Then we use the upper and lower solution method to give a monotonic iterative sequence of the generalized random impulsive Sturm–Liouville differential equations and prove that it is convergent. Finally, we give two concrete examples to verify the correctness of the results.

Halpern subgradient extragradient algorithm for solving quasimonotone variational inequality problems

In this paper, we study the numerical solution of the variational inequalities involving quasimonotone operators in infinite-dimensional Hilbert spaces. We prove that the iterative sequence generated by the proposed algorithm for the solution of quasimonotone variational inequalities converges strongly to a solution. The main advantage of the proposed iterative schemes is that it uses a monotone and non-monotone step size rule based on operator knowledge rather than its Lipschitz constant or some other line search method.

On the Positive Operator Solutions to an Operator Equation X − A ∗ X − t A = Q

In this paper, the positive operator solutions to operator equation X − A ∗ X − t A = Q (t > 1) are studied in infinite dimensional Hilbert space. Firstly, the range of norm and the spectral radius of the solution to the equation are given. Secondly, by constructing effective iterative sequence, it gives some conditions for the existence of positive operator solutions to operator equation X − A ∗ X − t A = Q (t > 1). The relations of these operators in the operator equation are given.

A New Sequential Optimality Condition of Cardinality-Constrained Optimization Problem and Application

In this paper, we consider the cardinality-constrained optimization problem and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results and is still a first-order necessity condition for the cardinality constraint problem without any additional assumptions. Meanwhile, we provide a problem-tailored weaker constraint qualification, which can guarantee that new sequential conditions are Mordukhovich-type stationary points. On the other hand, we improve the theoretical results of the augmented Lagrangian algorithm. Under the same condition as the existing results, we prove that any feasible accumulation point of the iterative sequence generated by the algorithm satisfies the new sequence optimality condition. Furthermore, the algorithm can converge to the Mordukhovich-type (essentially strong) stationary point if the problem-tailored constraint qualification is satisfied.

On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces

We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.

Application of chaotic encryption algorithm based on variable parameters in RFID security

In the development of the Internet of Things technology, RFID technology plays a very important role in the application of the Internet of Things. However, due to the safety problems caused by the non-contact sensing of the RFID system, the further development of RFID technology in the application is largely hindered. In recent years, chaotic encryption has been applied in the field of cryptography by virtue of its unique characteristics, and it has received more and more attention in the security of RFID data transmission. Using the same key for encryption and decryption operations is a lightweight encryption algorithm. However, there are various problems in the application process of chaotic encryption: (1) nonlinear dynamic characteristics degradation and short-cycle cycle problems will occur under the influence of computer limited accuracy; (2) numerical conversion operations are required during application, to a certain extent It will affect the randomness of the iterative sequence; (3) During the iterative process, the iterative sequence cannot be spread over the entire value interval, and the randomness is poor. This paper proposes an improved segmented Logistic mapping encryption algorithm, uses the m-sequence to perturb initial value and sets a fixed step to change the control parameter value to generate a chaotic key stream sequence, and applies it to the RFID system data transmission security mechanism to encrypt the data. Experimental simulation and performance analysis show that the iterated chaotic sequence has good random distribution characteristics, unpredictability, and traversability. Compared to the previous improvement, the key space is increased to reach the size of 1024 space and can meet the security needs, which improve RFID data security and can effectively avoid various security problems.

Positive solutions of a second-order nonlinear Robin problem involving the first-order derivative

This paper is concerned with the second-order nonlinear Robin problem involving the first-order derivative: $$ \textstyle\begin{cases} u''+f(t,u,u^{\prime })=0, \\ u(0)=u'(1)-\alpha u(1)=0,\end{cases} $$ { u ″ + f ( t , u , u ′ ) = 0 , u ( 0 ) = u ′ ( 1 ) − α u ( 1 ) = 0 , where $f\in C([0,1]\times \mathbb{R}^{2}_{+},\mathbb{R}_{+})$ f ∈ C ( [ 0 , 1 ] × R + 2 , R + ) and $\alpha \in ]0,1[$ α ∈ ] 0 , 1 [ . Based on a priori estimates, we use fixed point index theory to establish some results on existence, multiplicity and uniqueness of positive solutions thereof, with the unique positive solution being the limit of of an iterative sequence. The results presented here generalize and extend the corresponding ones for nonlinearities independent of the first-order derivative.

Improved inertial projection and contraction method for solving pseudomonotone variational inequality problems

The objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the proposed algorithm, and the strong convergence of the iterative sequence is obtained under some appropriate conditions. The main advantage of the algorithm is that the proof of convergence of the algorithm is implemented without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments are also put forward to support the analysis of the theorem and provide comparisons with related algorithms.

Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems

In this paper, we discuss the split monotone variational inclusion problem and propose two new inertial algorithms in infinite-dimensional Hilbert spaces. As well as, the iterative sequence by the proposed algorithms converges strongly to the solution of a certain variational inequality with the help of the hybrid steepest descent method. Furthermore, an adaptive step size criterion is considered in suggested algorithms to avoid the difficulty of calculating the operator norm. Finally, some numerical experiments show that our algorithms are realistic and summarize the known results.