Results on a faster iterative scheme for a generalized monotone asymptotically


  • Athraa Najeb Abed Dep. Of Math. Colle. Of Education for Pure Sciences Ibn Al-Haitham University of Baghdad
  • Salwa Salman Abed II Department of Mathematics, college of Education for pure science Ibn Al Haitham,



Banach space, fixed point, momotone mappings, α-nonexpansive mapping, iterative scheme


This article devoted to present results on convergence of  Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive  mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and  Σn+=1 λn= +∞, λ=min{hn , (1-hn)} where h⸦ (0,1)   where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status.


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Abdul Jabber, M. F., Abed, S. S. (2020). The convergence of iteration scheme to fixed points in modular spaces, Iraqi Journal of Science, vol.60, no,10, pp2197-2202.

Abed, S. S., Abdul Jabber, M. F. (2020). Approximating fixed points in moduler spaces, Karbala International Journal of Modern Science, vol.6,no.2, pp121-128.

Abed, S. S., Abdul Jabbar, M. F.( 2021). Some Results on Normalized Duality Mappings and Approximating Fixed points in Convex Real Moduler Spaces, Baghdad journal of science 18(4):1218-1225.DOI:

Abed, S. S., Abed, A. N. Convergence and stability of iterative scheme for a monotone a total asymptotically nonexpansive mapping, Accepted Iraqi Journal of science.

Abed, S. S., Mohamed Hasan, Z. M. (2019). Common fixed point of a finite-step iteration algorithm under total asymptotically quasi-nonexpansive maps, Baghdad Science Journal ,16(3),654-660.

Alber, YA. I., Chidume, C.E., Zegeye, H. (2006). Approximating fixed points of total asymptotically nonexpansive mappings", Fixed point Theory and Applications , article ld 10673,1-12.

Aoyama, K., Kohsaka, F. (2011). Fixed point theorem for -non-expansive mapping in Banach spaces .Nonlinear Anal.74,437-4391.

Aoyama, K., lemoto, S., Kohsaka, F., Takahashi, W. (2010). Fixed point and ergodic theorems for -hybrid mapping in Hilbert spaces . J. Nonlinear convex Anal.11, 335-343.

Aunpam, S., Mohammed, I. (2014). Approximating Fixed Point of Generalized Nonexpansinve Mappings Via Faster Iteration Schemes”Fixed point theory, No.4.605-623.

Bachar, M., Khamsi, M. A. (2015). On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces. Fixed point Theory Appl, 2015,160.

Browder, F. E. (1966). Semicontractive and Semiaccretive Nonlinear Mappings in Banach Spaces, Bull. Amer . Math. Soc 74,660-665.

Chidume, C. E., Ali, B. (2007). Weak and strong convergence theorems for finite families of asymptotically nonexpansive mapping in Banach spaces, J. Math, Anal. Appl . 330,377-387.

Dehaish, B. A., Khamsi, M. A. (2015). Mann iteration process for momotone nonexpansive mappings. Fixed Point Theory. Appl.2015,177.

Feng, G. U. (2006). Convergence of the implicit iterative process with errors for a finite family of asymptotically nonexpansive mappings, Acta Math. Sci. 26,1131-1143.

Goebel, K., Krik, W. A. (1972). Fixed point theorem for Asymptotically Nonexpansive Mapping , Proc. Amer. Math. Soc.35-171-174.

Harder, A. M., Hicks, T. L. (1988). Stability result for fixed point iteration procedures, Math . Japonica,33,693-706.

Khan, S. H., Kim, H. K. (2010). Common Fixed Point of two Nonexpansive Mappings Modified Faster Iteration Scheme, Bull. Korean. Math. Soc. 47,No.5,PP .973-985,DOI:10.4134/BKMS.

Lim, T .C., Xu, H. X. (1994). Fixed point theorems for asymptotically nonexpansive mappings. Nonl. Anal 22,1345-1355.

Malih, S. H., Abed, S. S. (2019). Approximating random fixed points under a new iterative sequence. J. of Inter. Math. Vol. 22, No. 8, pp. 1407–1414,DOI 10.1080/09720502.2019.1700927.

Malih, S. H., Abed, S. S. (2021). Convergence and stability of some random iterative scheme, accepted in ICPAS conference and accepted publication in IOP Journal of Physics.

Malih, S. H., Abed, S. S.(2021). Convergence of random iterative scheme to a common random fixed points, accepted in ICPAS conference and accepted publication in IOP Journal of Physics.

Mohamed Hasan, Z. M., Abed, S. S. (2019). Weak convergence of two iteration scheme in Banach spaces, Engineeeing and Technology Journal 37,B02,1-12.http://dx.doi.oeg/10.30684/eti.37.2B.1

Na, J., Tang, Y. (2014). Weak and strong convergence theorems of fixed points for total asymptotically nonexpansive multi-vaued mappings in Banach spaces.J. Appl . Math ,sci. 8,1903-1913.

Reich, S. (1980). Strong convergence theorems for resolvents of accretive operators in Banach spaces. J. Math. Anal. Appl.75,287-292.

Sahu, D. R., ORegan, D., Agarwal, R. P. (2009). Fixed Point Theory for Lipschitzain-type Mappings with Applications, Topological Fixed Point Theory and Its Applications ,Springer Science + Business. Media, LLC.

Saluja, G. S. (2014). Convergence to common fixed points for generalized asymptotically quasi-nonexpansive mappings. Bull. of the Inter. Math. Virtual Institute, 4,69-79doi:1.7251/BIMVI140169S.

Samanta, K. T., Sanjay, R., Bivas, D. (2010). Cone Normed Linear Spaces, West Bengal, India.

Song, Y. S., Promluang, K., Kumam, P., Cho, Y. J. (2016). Some convergence theorem of the Mann iteration for monotone α-non-expansive mapping ,Appl. Math. Comput., 287/288,74-82.

Sun, J. (2008). Nonlinear Functional Analysis and Its Application, Science Publishing House, Beijing.

Takahashi, W. (2009). Nonlinear Functional Analysis-Fixed Point Theory and its Applications , Yokohama Publishers Inc., Yokohama.

Tan, K. K., Xu, H. K., (1994). Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math .Soc. 122,733-739.

Timis, I. (2010). On the weak stability of Picard iteration for some contractive type mappings, Annal. Uni. Craiva, Math. Comput. Sci .Series,37,106-114.

Uddin, I., Garodia, C., Nieto, J. J. (2018). Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations ,Uddin et al. Journal of Ineqalities and Applications ,2018:339.

Weiping, G., Cho, Y. J. (2008). On the strong convergence of the implicit iterative processes with errors for a finite family of asymptotically nonexpansive mappings, Appl. Math. Lett. 21,1046-1052.

Zhou, Y. Y., Chang, S. S. (2002). convergence of the implicit iterative process with errors for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Anal. Appl. 23,911-921.




How to Cite

Abed, A. N., & Abed II, S. S. . (2021). Results on a faster iterative scheme for a generalized monotone asymptotically . JOURNAL OF ADVANCES IN MATHEMATICS, 20, 356–370.