Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces

Year 2020, Volume: 4 Issue: 2, 112 - 120, 30.06.2020

Gedala Satyanarayana , G. V. R. Babu

https://doi.org/10.31197/atnaa.649269

Abstract

We define SP-iteration procedure associated with three self maps T1; T2; T3 defined

on a nonempty convex subset of a convex metric space X and prove -convergence of

this iteration procedure to a common fixed point of T1; T2; T3 under the hypotheses that

each Ti is either an -nonexpansive map or a Suzuki nonexpansive map in the setting

of uniformly convex metric spaces. Also, we prove the strong convergence of this iteration

procedure to a common fixed point of T1; T2; T3 under certain additional hypotheses

namely either semicompact or condition (D).

Keywords

SP-iteration procedure, \alpha-nonexpansive map, Suzuki nonexpansive map, common fixed point, \delta-convergence, strong convergence, uniformly convex metric space

References

• Prof. Binayak S. Choudhury,Department of Mathematics,Bengal Engineering and Science University,Shibur, P. O.- B. Garden, Shibpur,West Bengal, India.E-mail: [e-mail]
• Prof. H. K. Pathak,School of studies in Mathematics,Pt. Ravishankar Shukla University,Chattisgarh, India.E-mail: [e-mail]
• Prof. P. P. Murthy,Department of Pure and Applied Mathematics,Guru Ghasi Das University,Chattisgarh, India.E-mail: [e-mail]