On set-valued nonlinear equations in Menger probabilistic normed spaces

• Published in: Fuzzy sets and systems Vol. 158; no. 16; pp. 1823 - 1831
• Main Author: MIHET, Dorel
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.08.2007; Elsevier
• Subjects: Applied sciences; Circuit properties; Computer science; control theory; systems; Control theory. Systems; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Fuzzy mappings; Information, signal and communications theory; Mathematical methods; Menger probabilistic normed spaces; Miscellaneous; Nonlinear operator equations; Probabilistic [formula omitted]-contractor couple; System theory; Telecommunications and information theory; Theoretical computing; Menger probabilistic normed spaces; Fuzzy mappings; Nonlinear operator equations; Probabilistic ϕ -contractor couple; Non linear equation; Engineering; Fuzzy system; Operator equation; Set valued operator; Information processing; Fuzzy set; Probabilistic p-contractor couple; Non linear operator
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2007.01.007

We introduce the concept of probabilistic ( ϕ , ψ ) -contractor couple, which allows us to consider set-valued nonlinear operator equations in a large class of probabilistic normed spaces. Our results complete those from Cho et al. [Nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 110 (2000) 115–122] and Fang [On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131 (2002) 357–364].