Suzuki-type fixed point theorem for fuzzy mappings in ordered metric spaces

Basit Ali,M Abbas

doi:10.1186/1687-1812-2013-9

Abstract

In this paper, a Suzuki-type fixed fuzzy point result for fuzzy mappings in complete ordered metric spaces is obtained. As an application, we establish the existence of coincidence fuzzy points and common fixed fuzzy points for a hybrid pair of a single-valued self-mapping and a fuzzy mapping. An example is also provided to support the main result presented herein.MSC:47H10, 47H04, 47H07.

Highlights

Introduction and preliminaries LetX be a space of points with generic elements of X denoted by x and I = [, ]
4 Conclusion The Banach contraction principle has become a classical tool to show the existence of solutions of functional equations in nonlinear analysis
Suzuki-type fixed point theorems for fuzzy mappings obtained in this article can further be used in the process of finding the solutions of functional equations involving fuzzy mappings in fuzzy systems

Summary

Then there exists a point x

Fx provided that satisfies the order sequential limit property. (c) gy ∈ F(x)α implies that (y, x) ∈ ∇. (d) (x, y) ∈ ∇ gives (u, v) ∈ ∇ whenever gu ∈ (Fx)α and gv ∈ (Fy)α. (e) (gx, gy) ∈ ∇ whenever (x, y) ∈ ∇ for all x, y ∈ X. If an ordered fuzzy hybrid pair {F, g} satisfies σ (r)pα(gx, Fx) ≤ d(gx, gy) implies Dα(Fx, Fy) ≤ rMα(F, g). F and g have a common fixed fuzzy point if any of the following conditions holds:. (g) g is F-fuzzy weakly commuting for some x ∈ Cα(g, F) and is a fixed point of g, that is, g x = gx. Using Theorem with a mapping A, it follows that A has a fixed fuzzy point u ∈ g(E). As (F(X))α ⊆ g(X), so there exists u ∈ X such that gu = u, it follows that gu ∈ (Agu )α = (Fu )α This implies that u ∈ X is a coincidence fuzzy point of F and g. (gx)α is a common fixed fuzzy point of F and g.

If x

Findings

Conclusion