zbMATH — the first resource for mathematics

Applications of the Ekeland type variational principles. (English) Zbl 1007.54031
Summary: J. S. Jung, Y. J. Cho, B. S. Lee, G. M. Lee, and H. K. Pathak [Panam. Math. J. 7, No. 3, 35-45 (1997; Zbl 0918.47047)] proved an infimum principle using an inductive method for sequences. In this paper, we show that improved versions of the main results of [Jung-Cho-Lee-Lee-Pathak, loc. cit.] are simple consequences of the Ekeland type variational principle due to S. Park [On generalizations of the Ekeland-type variational principles, Nonlinear Anal., Theory Methods Appl. 39 A, No. 7, 881-889 (2000; Zbl 1044.49500)].
54E50 Complete metric spaces
47H10 Fixed-point theorems
49J40 Variational inequalities
49J45 Methods involving semicontinuity and convergence; relaxation
49J53 Set-valued and variational analysis
47J30 Variational methods involving nonlinear operators