On fixed point of monotone (α, β)− nonexpansive mappings in ordered hyperbolic metric spaces

Authors

  • Kiran Department of Mathematics, Government Dudhadhari Bajrang Girls Postgraduate Autonomous College, Raipur (C.G.)

Keywords:

Fixed point, (α, β)− nonexpansive mapping, hyperbolic space

Abstract

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.

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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

24-04-2024

How to Cite

Kiran. (2024). On fixed point of monotone (α, β)− nonexpansive mappings in ordered hyperbolic metric spaces. Communications in Mathematics and Applications, 15(1). Retrieved from http://www.rgnpublications.com/journals/index.php/cma/article/view/2347

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Section

Research Article