On fixed point of monotone (α, β)− nonexpansive mappings in ordered hyperbolic metric spaces
Keywords:
Fixed point, (α, β)− nonexpansive mapping, hyperbolic spaceAbstract
This paper is concerned with convergence and ∆− convergence of a sequence generated by Picard-Mann hybrid iteration scheme for monotone (α, β)− nonexpansive type mappings in ordered hyperbolic metric spaces along with some fixed point results. Here we also put an application in L1([0, 1]) space.
Downloads
References
Aoyama K, Kohsaka F., Fixed point theorem for α− nonexpansive mappings in Banach spaces, Nonlinear Anal., Vol. 74, (2011), pp. 4387-4391.
Bachar M., Khamsi M.A., On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces, Fixed Point Theory Appl., Vol. 2015, (2015), pp. 1-11.
Dehaish B.A.B., Khamsi M.A., Mann iteration process for monotone nonexpansive mappings, Fixed Point Theory Appl., Vol. 2015, (2015), pp. 1-7.
Suzuki T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl., Vol. 340, (2008), pp. 1088-1095.
Muanchoo K., Kumam P. and et al., Fixed point theorems and convergence theorems for monotone (α, β)− nonexpansive mappings in ordered Banach spaces, Creat. Math. Infor., Vol. 26, no. 2, (2017), pp. 163-180.
Uddin i, Garodia C., Nietro J.J., Mann iteration for monotone nonexpansive mappings in ordred CAT(0) space with an application to integral equations, J. Ineq. Appl., Vol. 2018, no. 1, (2018), pp. 1-18.
Kohlenbach U., Some logical metatheorems with applications in functional analysis, Tran. Amer. Math. Soc., 357(1) (2004), 89-128.
Chang S., Wang G., et al., ∆−Convergence theorems for multi-valued nonexpansive mappings in hyperbolic spaces, Appl. Math. Comput., Vol. 249, (2014), pp. 535-540.
Kasloom A., Saleem N. et al., Fixed point approximation of monotone nonexpansive mappings in hyperbolic spaces, J. Function Spaces, Vol. 2021, (2021), pp. 1-14.
Kasloom A., Rashid M., Sun T. et al., Fixed points of monotone total asymptotically nonexpansive mappings in hyperbolic spaces via new algorithm, J. Function Spaces, (2021), 1-10.
Suanoom C., Klin-eam C., Remark on fundamentally nonexpansive mappings in hyperbolic spaces, Bull. Aust. J. Nonlinear Sci. Appl., Vol. 9, (2016), 1952-1956.
B. A. Bin Dehaish and M. A. Khamsi, “Browder and G¨ohde fixed point theorem for monotone nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2016, no. 1, (2016), pp. 1-9.
Leustean L., Nonexpansive iteration in uniformly convex W− hyperboloc spaces, In A. Leizarowitz, B.S. Mordukhovich, I. Shafrir, A. Zaslavski, Nonlinear Analysis and Optimization I. Nonlinear analysis contemporary Mathematics, Providence, RI Ramat Gan American Mathematical Soc., Bar Ilan Uni., Vol. 513, (2010), pp. 193-210.
Khan S.H., A Picard-Mann hybrid iterative process, Fixed Point Theory and Appl., Vol. 2013 ,(2013), pp. 1-10.
Song Y, Kumam P., et al., Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces, Fixed Point Theory and Appl., (2016), pp. 1-11.
Khamsi M.A., Khan A.R., On monotone nonexpansive mappings in L1([0, 1]), Fixed Point Theory and Appl., (2015), pp. 1-5.
Mann W.R., Mean value methods in iteration, Pro. Amer. Math. Soc., Vol. 4, (1953), pp. 506-510.
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.