We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

The two-operator split common fixed point problem (two-operator SCFP) with firmly nonexpansive mappings is investigated in this paper. This problem covers the problems of split feasibility, convex feasibility, and equilibrium and can especially be used to model significant image recovery problems such as the intensity-modulated radiation therapy, computed tomography, and the sensor network. An iterative scheme is presented to approximate the minimum norm solution of the two-operator SCFP problem. The performance of the presented algorithm is compared with that of the last algorithm for the two-operator SCFP and the advantage of the presented algorithm is shown through the numerical result.

An existence result for the solution set of symmetric vector quasi-equilibrium problems that allows for discontinuities is obtained. Moreover, sufficient conditions for the generalized Levitin-Polyak well-posedness of symmetric vector quasi-equilibrium problems are established.

A finite-step iteration sequence for two finite families of asymptotically nonexpansive mappings is introduced and the weak and strong convergence theorems are proved in Banach space. The results presented in the paper generalize and unify some important known results of relevant scholars.

The concept of Levitin-Polyak well-posedness of an equilibrium-like problem in Banach spaces is introduced. Under suitable conditions, some characterizations of its Levitin-Polyak well-posedness are established. Some conditions under which an equilibrium-like problem in Banach spaces is Levitin-Polyak well-posed are also derived.

We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.

We propose a new method to solve nonlinear semidefinite complementarity problem by combining a continuous method and a trust-region-type method. At every iteration, we need to calculate a second-order cone subproblem. We show the well-definedness of the method. The global convergent result is established.

The class 𝔄-$KKM(X,Y,Z)$ and generalized $KKM$ mapping are introduced, and some generalized $KKM$ theorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.

We first propose a new concept of GFC-subspace. Using this notion, we obtain a new continuous selection theorem. As a consequence, we establish some new collective fixed point theorems and coincidence theorems in product GFC-spaces. Finally, we give some applications of our theorems.

The existence of equilibrium points, and the essential stability of the set of equilibrium points of the equilibrium problem with lower and upper bounds are studied on Hadamard manifolds.

We consider the global error bound for the generalized nonlinear complementarity problem over a polyhedral cone (GNCP). By a new technique, we establish an easier computed global error bound for the GNCP under weaker conditions, which improves the result obtained by Sun and Wang (2013) for GNCP.

This paper is devoted to the various coercivity conditions in order to guarantee existence of solutions and boundedness of the solution set for the variational-hemivariational inequalities involving upper semicontinuous operators. The results presented in this paper generalize and improve some known results.

We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. Under suitable conditions, the existence of solutions for the system of multivalued mixed variational inequality problem and the convergence of iterative sequences generated by the generalized $f$-projection algorithm are proved. A perturbational algorithm for solving a special case of multivalued mixed variational inequality problem is formally constructed. The results concerned with the existence of solutions and the convergence of iterative sequences generated by the perturbational algorithm are also given. Some known results are improved and generalized.

By using a nonlinear scalarization technique, the bounded rationality model $M$ for generalized abstract fuzzy economies in finite continuous spaces is established. Furthermore, by using the model $M$, some new theorems for structural stability and robustness to ($\lambda ,ϵ$)-equilibria of generalized abstract fuzzy economies are proved.