Fixed Point Results for \((\alpha\)-\(\beta_k,\phi\)-\(\psi)\) Integral Type Contraction Mappings in Fuzzy Metrics

Rakesh Tiwari, Shraddha Rajput


In this paper, we introduce the notion of a modified \((\alpha\)-\(\beta_k,\phi\)-\(\psi)\) integral type contraction mappings in fuzzy metric spaces. We study and prove the existence and uniqueness of fixed points theorems in generalized fuzzy contractive mappings of integral type in fuzzy metric spaces. Our main result generalizes the fuzzy Banach contraction theorem and we validate our results by some suitable examples which reveal that our results are proper generalization and modification of some researchers' integral contraction works.


Fixed point; Metric spaces; Fuzzy metric spaces; Integral type contraction; Modified \((\alpha\)-\(\beta_k,\phi\)-\(\psi)\) Contraction

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