Abstract. In this paper, we consider a generalized mixed set-valued variational inequality problem which includes many important known variational inequality problems and equilibrium problem, and its related some auxiliary variational inequality problems. We prove the existence of solutions of the auxiliary variational inequality problems and suggest a two-step iterative algorithm and an inertial proximal iterative algorithm. Further, we discuss the convergence analysis of iterative algorithms. The theorems presented in this paper improve and generalize many known results for solving equilibrium problems, variational inequality and complementarity problems in the literature.
Abstract:In this paper we study the qualitative properties and the periodic nature of the solutions of the difference equationwhere the initial conditions x −5 , x −4 , x −3 , x −2 , x −1 , x 0 are arbitrary positive real numbers and α, β, γ, δ are positive constants. In addition, we derive the form of the solutions of some special cases of this equation.
Discrete models are versatile and effective tools for assessing and addressing a wide range of scientific and practical problems. As a type of discrete model, the difference equation model has been widely employed in domains such as algorithm analysis, signal processing, biology, economics, and computer science. The global dynamical behavior of a class of discrete models known as the max-type difference equation model is the subject of the research. The purpose of this work is to look into the behavior of the solution of the following four-order max-type difference equation:
z
i
+
1
=
max
A
i
/
z
i
,
z
i
−
3
,
i
=
0,1,2
,
…
.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.