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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {371 },
     year = {2019},
     volume = {43},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_3_a2/}
}
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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/