Shih-sen Chang

Some problems and results in the study of nonlinear analysis

This paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis, which were obtained by the author and some Chinese mathematicians.

Coincidence point theorems and minimization theorems in fuzzy metric spaces

Abstract In this paper, some new versions of coincidence point theorems and minimization theorems for single-valued and multi-valued mappings in generating spaces of the quasi-metric family are obtained. As applications, we utilize our main theorems to prove coincidence point theorems, fixed point theorems and minimization theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

Approximating solutions of variational inequalities for asymptotically nonexpansive mappings

By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of iterative sequences to converging to a fixed point which is also the unique solution of some variational inequalities are obtained. The results presented in the paper extend and improve some recent results in [C.E. Chidume, Jinlu Li, A. Udomene, Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 138 (2) (2005) 473-480; N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006) 558-567; T.C. Lim, H.K. Xu, Fixed point theories for asymptotically nonexpansive mappings, Nonlinear Anal. TMA, 22 (1994) 1345-1355; H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004) 279-291].

On the existence of periodic solutions for nonlinear evolutions in Hilbert spaces

A periodic solutions for nonlinear evolution equations of the form du/dt ∈ -Au(t) + F(t,u(t)), t ∈ R, where F : R × H → 2 is a set-valued Caratheodory function are considered when both F and A are set-valued mappings and not necessarily linear.