Browse > Article
http://dx.doi.org/10.22771/nfaa.2021.26.05.07

CONVERGENCE THEOREMS FOR SP-ITERATION SCHEME IN A ORDERED HYPERBOLIC METRIC SPACE  

Aggarwal, Sajan (Department of Mathematics, Jamia Millia Islamia)
Uddin, Izhar (Department of Mathematics, Jamia Millia Islamia)
Mujahid, Samad (Department of Mathematics, Jamia Millia Islamia)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.5, 2021 , pp. 961-969 More about this Journal
Abstract
In this paper, we study the ∆-convergence and strong convergence of SP-iteration scheme involving a nonexpansive mapping in partially ordered hyperbolic metric spaces. Also, we give an example to support our main result and compare SP-iteration scheme with the Mann iteration and Ishikawa iteration scheme. Thus, we generalize many previous results.
Keywords
Hyperbolic space; SP-iteration;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. Shimizu and W. Takahashi, Fixed points of multivalued mapping in certain convex metric space, Tolol Methds Nonlinear Anal., 8 (1996), 197-203.
2 S. Aggarwal, I. Uddin and J.J. Nieto, A fixed-point theorem for monotone nearly asymptotically nonexpansive mappings, J. Fixed Point Theory Appl., (2019), 21:91.
3 S. Aggarwal and I. Uddin, Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping, Demonstratio Math., 52 (2019), 388-396.   DOI
4 J. Ali and I. Uddin, Convergence of SP-iteration for generalized nonexpansive mapping in Banach spaces, Ukrainian Math. J., 73(6) (2021), 738-748.
5 H. Fukhar-ud-din and M.A. Khamsi, Approximating common fixed pint in hyperbolic spaces, Fixed Point Theory Appl., (2014), 2014:113.
6 D. Gohde, Zum Prinzip der kontraktiven Abbildung, Math. Nachr., 30 (1965), 251-258.   DOI
7 S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.   DOI
8 W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly, 72 (1965), 1004-1006.   DOI
9 T.C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60 (1976), 179-182.   DOI
10 L. Leustean, Nonexpansive iterations in uniformly convex W-hyperbolic spaces, in A. Leizarowitz, B. S. Mordukhovich, I. Shafrir and A. Zaslavski, (Eds). Nonlinear Analysis and Optimization I: Nonlinear Analysis, Contemp. Math., Amer. Math. Soc., 513 (2010), 193-209.
11 J.J. Nieto and R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order, 22 (2005), 223-239.   DOI
12 M.A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229.   DOI
13 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.   DOI
14 A.C.M. Ran and M.C.B. Reuring, A fixed point theorems in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., Vol. 132 (2005), 1435-1443.   DOI
15 W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510.   DOI
16 F.E. Browder, Fixed point theorems for noncompact mappings in Hilbert Space, Proc. Nat. Acad. Sci. USA., 53 (1965), 1272-1276.   DOI
17 C. Garodia and I. Uddin, A new iterative method for solving split feasibility problem, J. Appl. Anal. Comput., 10(3) (2020), 986-1004.
18 U. Kohlenbach, Some logical metatheorems with application in functional analysis, Trans. Amer. Math. Soc., 357 (2005), 89-128.   DOI
19 R.P. Agarwal, D.O. Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal., 8 (2007), 61-79.
20 C. Garodia and I. Uddin, A new fixed point algorithm for finding the solution of a delay differential equation, AIMS Mathematics, 5(4) (2020), 3182-3200.   DOI
21 F.E. Browder, Nonexpansive nonlinear operators in a Banach Space, Proc. Nat. Acad. Sci. USA., 54 (1965), 1041-1044.   DOI