Common fixed points in best approximation for Banach operator pairs with C´ iric´ type I -contractions

The common fixed point theorems, similar to those of C´ iric´ [Lj.B. C´ iric´, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174–178; Lj.B. C´ iric´, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145–152; Lj.B. C´ iric´, 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, Internat. 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 C´ iric´ 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. © 2007 Elsevier Inc. All rights reserved.