Geodesic
Fixed Point Theorems Under $\omega$-distance Functions and Applications to Nonlinear Integral and Fractional Differential Equations
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 371

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we utilize the family $\mathfrak{F}$ and the notion of $\omega$-distance in an ordered $\mathcal{G}$-metric space and introduce $(F,\omega)$-contractions in order to derive some fixed point results. We also discuss the problems of Ulam-Hyers stability, well-posedness and limit shadowing property. In order to illustrate the use of our results, we apply them to nonlinear integral equations, as well as to some three-point fractional integral boundary value problems, both with numerical examples.
Classification : 47H10 47H09
Keywords: Fixed point, partially ordered set, $\mathcalG$-metric space, $\omega$-distance function, Ulam-Hyers stability, fractional integral boundary value problem 
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     author = {H. K. Nashine and R. K. Vats and Z. Kadelburg},
     title = {Fixed {Point} {Theorems} {Under} $\omega$-distance {Functions} and {Applications} to {Nonlinear} {Integral} and {Fractional} {Differential} {Equations}},
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H. K. Nashine; R. K. Vats; Z. Kadelburg. Fixed Point Theorems Under $\omega$-distance Functions and Applications to Nonlinear Integral and Fractional Differential Equations. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 3, p. 371 . http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a2/