Abstract
In this article, our aim is to consider a class of fuzzy mixed variational-like inequalities (FMVLIs) for fuzzy mapping known as extended perturbed fuzzy mixed variational-like inequalities (EPFMVLIs). As exceptional cases, some new and classically defined “FMVLIs” are also attained. We have also studied the auxiliary principle technique of auxiliary “EPFMVLI” for “EPFMVLI.” By using this technique and some new analytic results, some existence results and efficient numerical techniques of “EPFMVLI” are established. Some advanced and innovative iterative algorithms are also obtained, and the convergence criterion of iterative sequences generated by algorithms is also proven. In the end, some new and previously known existence results and algorithms are also studied. Results secured in this paper can be regarded as purification and development of previously familiar results.
Highlights
It has been verified that fuzzy optimality conditions of differentiable fuzzy preinvex mappings can be distinguished by variational-like inequalities
We shall introduce and discuss a new type of “GMVLI” for fuzzy mappings, which is known as extended perturbed fuzzy mixed variational-like inequality (EPFMVLI) for fuzzy mapping because by using this technique, we can handle the functional which is the sum of differentiable preinvex fuzzy mapping and strongly preinvex fuzzy mapping and their special cases like the single-valued functional which is the sum of the differentiable preinvex functions and strongly preinvex functions
We review the Auxiliary problem associated with “EPFMVLI” (5) and prove an existence theorem for the auxiliary problem
Summary
Let J be a real Hilbert space and ∅ ≠ C ⊂ J be a convex set. We denote the collection CB(J) of all nonempty bounded and closed subsets of J, and D(., .)is the Hausdorff metric on CB(J) defined by. A closed fuzzy mapping P: J ⟶ F(J) is said to satisfy the condition (B), if there exists a function P: J ⟶ [0, 1] such that for each u ∈ J, the set. Where P, V: C ⟶ F(J)are two closed fuzzy mappings satisfying condition (B) with function r, s: J ⟶ [0, 1], respectively, such that. If fuzzy mappings P, V: J ⟶ F(J) are closed and fulfil the condition (B) with functions r, s: J ⟶ [0, 1], nonlinear mapping M(., .): J × J ⟶ J is said to be (i) c-L-continuous in respect of first argument if for any u1, u2 ∈ Jand p1 ∈ [Pu1]r(u1), u2 ∈ [Pu2]r(u2), there exists a constant c > 0 such that.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
