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

The common fixed point theorems, similar to those of Ćirić [Lj.B. Ćirić, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174–178; Lj.B. Ćirić, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145–152; Lj.B. Ćirić, 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 Ćirić 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.