Application of fixed point theorems to best simultaneous approximation in ordered semi-convex structure

Volume 5, Issue 4, pp 294--306 http://dx.doi.org/10.22436/jnsa.005.04.05

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Authors

N. Hussain - King Abdul Aziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. H. K. Pathak - School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, (C. G.), 492010, India. S. Tiwari - Shri Shankaracharya Institute of Professional Management and Technology, Raipur, (C. G.), 492010, India.

Abstract

In this paper, we establish some common fixed point results for uniformly \(C_q\)-commuting asymptotically S-nonexpansive maps in a Banach space with semi-convex structure. We also extend the main results of Ćirić [Lj. B. Ćirić, Publ. Inst. Math., 49 (1991), 174-178] and [Lj. B. Ćirić, Arch. Math. (BRNO), 29 (1993), 145-152] to semi-convex structure and obtain common fixed point results for Banach operator pair. The existence of invariant best simultaneous approximation in ordered semi-convex structure is also established.

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Keywords

• Common fixed point
• uniformly \(C_q\)-commuting
• asymptotically S-nonexpansive map
• Banach operator pair
• best simultaneous approximation

MSC

•  47H10
•  54H25

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