Random iterative algorithms for nonlinear mixed family of random fuzzy and crisp operator equation couples in fuzzy normed spaces (Q2912665)

By using a random version of the theory of \((\varphi -\psi )\)-contractor due to \textit{D. Miheţ} [Fuzzy Sets Syst. 158, No.~16, 1823--1831 (2007; Zbl 1116.47062)], the authors introduce and study a new class of nonlinear mixed families of random fuzzy and crisp operator equation couples in fuzzy normed spaces. They construct some new random iterative algorithms for solving this kind of nonlinear operator equation couples in fuzzy normed spaces and prove the convergence of iterative sequences generated by the algorithms under joint orbitally complete conditions. As applications, they prove some new common fixed point theorems for fuzzy and crisp operators in fuzzy normed spaces.NEWLINENEWLINEThe results presented in this paper improve and generalize corresponding results of \textit{Y. J. Cho}, \textit{H.-Y. Lan} and \textit{N.-J. Huang} [J. Inequal. Appl. 2010, Article ID 152978 (2010; Zbl 1189.47084)], \textit{J.-X. Fang} and \textit{G.-A. Song} [Fuzzy Sets Syst. 121, No. 2, 267--273 (2001; Zbl 1008.47070)], \textit{S. S. Chang} et al. [J. Comput. Anal. Appl. 8, No. 2, 139--149 (2006; Zbl 1115.49006)], \textit{D. Turkoglu} et al. [J. Appl. Math. Comput. 22, No. 1--2, 411--424 (2006; Zbl 1106.54020)], \textit{B. K. Sharma}, \textit{D. R. Sahu} and \textit{M. Bounias} [Fuzzy Sets Syst. 125, No. 2, 261--268 (2002; Zbl 0987.54050)], \textit{D. Miheţ} [Fuzzy Sets Syst. 158, No. 16, 1823--1831 (2007; Zbl 1116.47062)], \textit{H.-Y. Lan} et al. [Lect. Notes Comp. Sci. 6401, 228--233 (2010 (2010; Zbl 1279.47087)], \textit{N.-J. Huang} and \textit{H.-Y. Lan} [Fuzzy Sets Syst. 152, No. 2, 209--222 (2005; Zbl 1101.47060)].