Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:338

Article

Hussain, N.¹ 

[1] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

关键词: common fixed points;    compatible maps;    Banach operator pair;    contractive condition of Ciric type;    best approximation;   

DOI  :  10.1016/j.jmaa.2007.06.008

来源: Elsevier

【 摘 要 】

The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Intemat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings. (C) 2007 Elsevier Inc. All fights reserved.

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