Approximation results for generalized (α, β)-nonexpansive type 1 mapping in hyperbolic metric spaces

[1] A.R.Khan, H.Fukhar-ud-din, and M.A.Khan, An implicit algorithm for two finite families of nonexpansive maps in  hyperbolic spaces, Fixed Point Theory Appl., (2012), Article ID 54.
[2] A.Sahin, E.Ozturk and G.Aggarwal, Some fixed point results for the KF-iteration process in hyperbolic metric spaces, Symmetry, 15 (2023), 1360. https://doi.org/10.3390/sym15071360.
[3] B.S.Thakur, D.Thakur and M.Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings, Appl. Math. Comput., 275 (2016), 147–155.
[4] C.Suanoom and C.Klin-eam , Remark on fundamentally non-expansive mappings in hyperbolic spaces, J. Nonlinear Sci. Appl., 9 (2016), 1952–1956.
[5] D.R.Sahu and A. Petrusel, Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces, Nonlinear Anal. Theory Methods Appl., 74 (2011), 6012-6023.
[6] F.Akutsah and O.K.Narain, On generalized (α, β)- nonexpansive mappings in Banach spaces with applications, Nonlinear Funct. Anal. Appl., 26 (2021), 663–684.
[7] F.Gursoy and V.Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, arXiv preprint arXiv:1403.2546 (2014).
[8] I.Karahan and M.Ozdemir, A general iterative method for approximation of fixed points and their applications, Adv. Fixed Point Theory, 3 (2013).
[9] J.B.Diaz and F.T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bull. Am. Math. Soc., 73 (1967), 516–519.
[10] J.G.Falset, E.L. Fuster and T.Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl., 375 (2011), 185–195.
[11] K.Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, Marcel Dekker: New York, NY, USA, 1984.
[12] L.Leustean, Nonexpansive iterations in uniformly convex W-hyperbolic spaces, In Nonlinear Analysis and  Optimization I: Nonlinear Analysis; Leizarowitz, A., Mordukhovich, B.S., Shafrir, I., Zaslavski, A. J., Eds.; Contemporary Mathematics; Israel Math. Conf. Proc.; American Mathematical Society: Providence, RI, USA; Bar Ilan University: Ramat-Gan, Israel, 513 (2010), 193–210.
[13] M.A.Krasnosel’skii, Two observations about the method of successive approximations, Usp. Mat. Nauk., 10 (1955), 123–127.
[14] M.Bridson and A.Haefliger, Metric Spaces of Non-Positive Curvature, Springer, Berlin, Germany, 1999.
[15] M.Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesn., 66 (2014), 223-234.
[16] M.A.Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251(2000), 217-229.
[17] O.Sahu and A.Banerjee, Convergence of Panigrahy iteration Process for Suzuki generalized Nonexpansive mapping in uniformly convex Banach space , Journal of Hyperstructures, 13 (2024), 94-108.
[18] R.Pant and R. Shukla, Approximating fixed points of generalized α nonexpansive mappings in Banach spaces, Numer. Funct. Anal.Opt., 8 (2017), 248–266.
[19] R.Chugh and S.Kumar, Strong Convergence of a new three step iterative scheme in Banach spaces, Am. J. Comput., 2 (2012), 345–357.
[20] R.P. Agarwal, D. Oregan, and D.R.Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Convex Anal., 8 (2007), 61-79.
[21] S.H.Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory Appl. (2013), Article ID 69.
[22] S.Ishikawa, Fixed points by new iteration method Proc. Amer. Math. Soc., 149(1974), 147-150.
[23] S.Reich and I.Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal., 15 (1990), 537–558.
[24] S.M.Soltuz and T. Grosan, Data dependence for Ishikawa iteration when dealing with contractive-like operators, Fixed Point Theory Appl., (2008).
[25] S.M.Soltuz, Data dependence for Ishikawa iteration. Lecturas Matem´aticas, 25 (2004), 149- 155. 
[26] S.I.Timi, On the weak stability of Picard iteration for some contractive type mappings, Annal. Uni. Craiova Math. Comput. Sci. Ser., 37 (2010), 106–114.
[27] S.Zhang, About fixed point theory for mean nonexpansive mapping in Banach spaces, J. Sichuan Normal Univ. Nat. Sci., 2 (1975), 67–68.
[28] T.Suzuki,Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl., 340 (2008), 1088–1095.
[29] T.Shimizu and W.Takahashi, Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal., 8 (1996),197–203.
[30] T.C.Lim, Remarks on some fixed point theorems, Proc. Am. Math. Soc., 60 (1976), 179–182.
[31] T.Cardinali and P.Rubbioni, A generalization of the Caristi fixed point theorem in metric spaces, Fixed Point Theory, 11 (2010),3–10.
[32] U.Kohlenbach, Some logical metatheorems with applications in functional analysis, Trans. Am. Math. Soc.,357 (2004), 89–128.
[33] V.Berinde, Iterative Approximation of Fixed Points, Springer Berlin, Germany, 2007.
[34] W.Phuengrattana and S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for  continuous functions on an arbitrary interval, J. Comput. Appl. Math., 235 (2011), 3006-3014.
[35] W.R.Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510.
[36] W.Takahashi, A convexity in metric spaces and nonexpansive mappings, Kodai Math. Semin. Rep., 22 (1970), 142–149.