In this paper, new classes of rational Geraghty contractive mappings in the setup of b-metric spaces are introduced. Moreover, the existence of some fixed point for such mappings in ordered b-metric spaces are investigated. Also, some examples are provided to illustrate the results presented herein. Finally, an application of the main result is given.for all x, y, z ∈ X.In this case, the pair (X, d) is called a b-metric space.The following example (corrected from []) illustrates that a b-metric need not be a continuous function.if one of m, n is even and the other is even or ∞, , if one of m, n is odd and the other is odd (and m = n) or ∞, , otherwise.
In this paper, we introduce the structure of S p-metric spaces as a generalization of both S-metric and S b-metric spaces. Also, we present the notions of S-contractive mappings in the setup of ordered S p-metric spaces and investigate the existence of a fixed point for such mappings under various contractive conditions. We provide examples to illustrate the results presented herein. An application to periodic boundary value problems is presented.
In this paper, we introduce generalized
α
-
η
-fuzzy contractive mappings and generalized
β
-
ζ
-fuzzy contractive mappings and prove existence of fixed point for such mappings. Our results generalize and improve the recent work of Gopal and Vetro (Iranian journal of fuzzy systems, 11 (2014), 95–107). Some equivalent conditions of our results are presented. Also, an example is given to support our new results.
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