Mixed variational inequalities with various error bounds for random fuzzy mappings

Article type: Research Article

Authors: Khan, Suhel Ahmad^{a; *} | Cholamjiak, Watcharaporn^b

Affiliations: [a] Department of Mathematics, BITS-Pilani, Dubai Campus, Dubai, UAE | [b] School of Science, University of Phayao, Phayao, Thailand

Correspondence: [*] Corresponding author. Suhel Ahmad Khan, Department of Mathematics, BITS-Pilani, Dubai Campus, UAE. Tel.: +00971558503105; Fax: +971 4 4200555; E-mail: [email protected].

Abstract: In this paper we establish various gap functions of random mixed variational inequalities in fuzzy environment and then by using the resolvent operator technique, error bounds and global error bounds are derived in terms of regularized and D-gap functions. Finally, we obtain error bounds for random mixed variational inequalities without using Lipschitz continuity assumption. Our work generalizes the previously known results for random variational inequalities.

Keywords: Gap function, random fuzzy function, resolvent operator, strongly mixed monotone, error bound

DOI: 10.3233/JIFS-171370

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2313-2324, 2018