Abstract
AbstractIn this paper, first we introduce certain new classes of Suzuki type contractions in triangular and non-Archimedean fuzzy metric spaces. Further we establish fixed point theorems for such kind of mappings in non-Archimedean and triangular fuzzy metric spaces. We also prove Suzuki type fixed point results in non-Archimedean and triangular ordered fuzzy metric spaces. The results presented here improve and generalize certain recent results from the literature. Two illustrative examples and an application to integral equations are given to support the usability of our results.
Highlights
Introduction and preliminariesThe concept of fuzzy metric space was introduced in different ways by some authors and further to this, the fixed point theory in this kind of spaces has been intensively studied
The applications of fixed point theorems are remarkable in different disciplines of mathematics, engineering and economics in dealing with problems arising in approximation theory, game theory and many others
Samet et al [ ] introduced the concepts of α-ψ-contractive and α-admissible mappings and established various fixed point theorems for such mappings defined on complete metric spaces
Summary
X is a complete fuzzy metric space, there exists x∗ ∈ X such that xn → x∗ as n → ∞. Suppose that there exists n ∈ N such that. X∗, t = max M(xn, xn+ , t), M x∗, fx∗, t , M xn, fx∗, t , M x∗, xn+ , t , and so lim Qf n→∞. Assume that there exists t such that M(x∗, fx∗, t ) ; i.e., x∗ = fx∗. (M, X, ) is a complete triangular fuzzy metric space.
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