**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30999

##### Two-step Iterative Process For Common Fixed Points of Two Asymptotically Quasi-nonexpansive Mappings

**Authors:**
Safeer Hussain Khan

**Abstract:**

**Keywords:**
Asypmtotically quasi-nonexpansive mappings,
Commonfixed point,
Strong and weak convergence,
Iteration process

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1075122

**References:**

[1] R.P.Agarwal, Donal O-Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonliear Convex. Anal.8(1)(2007), 61-79.

[2] L.C. Deng, P. Cubiotti, J.C. Yao, Approximation of common fixed points of families of nonexpansive mappings, Taiwanese J. Math. 12 (2008) 487-500.

[3] L.C. Deng, P. Cubiotti, J.C. Yao, An implicit iteration scheme for monotone variational inequalities and fixed point problems, Nonlinear Anal. 69 (2008) 2445-2457.

[4] L.C. Deng, S. Schaible, J.C. Yao, Implicit iteration scheme with perturbed mapping for equilibrium problems and fixed point problems of finitely many nonexpansive mappings, J. Optim. Theory Appl. 139 (2008) 403-418.

[5] Y. J. , H. Y. Zhou and G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47(2004), 707-717.

[6] G. Das and J. P. Debata, Fixed points of Quasi-nonexpansive mappings, Indian J. Pure. Appl. Math., 17 (1986), 1263-1269.

[7] H. Fukhar-ud-din and S. H. Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328 (2007), 821-829.

[8] K.Goebel and W.A.Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc.35(1972), 171-174.

[9] S. H. Khan, Y.J. , M. Abbas, Convergence to common fixed points by a modified iteration process, Journal of Appl. Math. and Comput. doi: 10.1007/s12190-010-0381-z.

[10] S. H. Khan, J.K. Kim,Common fixed points of two nonexpansive mappings by a modified faster iteration scheme , Bull. Korean Math. Soc. 47 (2010), No. 5, pp. 973-985, DOI 10.4134/BKMS.2010.47.5.973

[11] S. H. Khan andW. Takahashi, Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Jpn., 53(1) (2001), 143-148.

[12] K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modifies Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006) 320-334.

[13] W. Nilsrakoo, S. Saejung, A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings, Comput. Math. Appl. 181 (2006) 1026-1034.

[14] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591-597.

[15] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159.

[16] W. Takahashi and G.E.Kim, Approximatig fixed points of nonexpansive mappings in Banach spaces , Math.Japonoica 48 1(1998), 1-9.

[17] N. Shahzad, H. Zegeye, Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps, Appl. Math. Comput. 189 (2007) 1058-1065.

[18] W. Takahashi, Iterative methods for approximation of fixed points and their applications, J.Oper.Res.Soc. Jpn., 43(1) (2000), 87 -108.

[19] W. Takahashi and T. Tamura, Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces, J.Approx.Theory , 91(3) (1997), 386 -397.

[20] K.K. Tan, H.K. Xu, Approximating fixed points of nonexpansive mappings by Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993) 301-308.