Geodesic
Generalized Suzuki Type $\mathcal Z$-Contraction in Complete Metric Spaces
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 419 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 introduce the notion of Suzuki type $\mathcal{Z}$-contraction and study the corresponding fixed point property. This kind of contraction generalizes the Banach contraction and unifies several known type of nonlinear contractions. We consider a nonlinear operator satisfying a nonlinear contraction in a metric space and prove fixed point results. As an application, we apply our result to show the solvability of nonlinear Hammerstein integral equations.
Classification : 47H09 47H10, 37C25
Keywords: Suzuki type $\mathcalZ$-contraction, fixed point, metric space, nonlinear Hammerstein integral equations 
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     author = {A. Padcharoen and P. Kumam and P. Saipara and P. Chaipunya},
     title = {Generalized {Suzuki} {Type} $\mathcal Z${-Contraction} in {Complete} {Metric} {Spaces}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {419 },
     year = {2018},
     volume = {42},
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     language = {en},
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A. Padcharoen; P. Kumam; P. Saipara; P. Chaipunya. Generalized Suzuki Type $\mathcal Z$-Contraction in Complete Metric Spaces. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 419 . http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a7/