Common fixed points and invariant approximation for Gregus type contraction mappings

Some new common fixed point theorems for Gregus type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these types of mappings are obtained. The proved results generalize, unify and extend some of the known results of M.A. Al-Thagafi (Int. J. Math. Sci. 18:613–616, 1995; J. Approx. Theory 85:318–323, 1996), M.A. Al-Thagafi and N. Shahzad (Nonlinear Anal. 64:2778–2786, 2006), L. ?iri? (Publ. Inst. Math. 49:174–178, 1991; Arch. Math. (BRNO) 29:145–152, 1993), M.L. Diviccaro, B. Fisher, S. Sessa (Publ. Math. (Debr.) 34:83–89, 1987), B. Fisher and S. Sessa (Int. J. Math. Math. 9:23–28, 1986), M. Gregus (Boll. Un. Mat. Ital. (5) 7-A:193–198, 1980), L. Habiniak (J. Approx. Theory 56:241–244, 1989), N. Hussain, B.E. Rhoades and G. Jungck (Numer. Func. Anal. Optim. 28:1139–1151, 2007), G. Jungck (Int. J. Math. Math. Sci. 13:497–500, 1990), G. Jungck and S. Sessa (Math. Jpn. 42:249–252, 1995), R.N. Mukherjee and V. Verma (Math. Jpn. 33:745–749, 1988), T.D. Narang and S. Chandok (Ukr. Math. J. 62:1367–1376, 2010), S.A. Sahab, M.S. Khan and S. Sessa (J. Approx. Theory 55:349–351, 1988), N. Shahzad (J. Math. Anal. Appl. 257:39–45, 2001; Rad. Math. 10:77–83, 2001; Int. J. Math. Game Theory Algebra 13:157–159, 2003), S.P. Singh (J. Approx. Theory 25:89–90, 1979), A. Smoluk (Mat. Stosow. 17:17–22, 1981), P.V. Subrahmanyam (J. Approx. Theory 20:165–172, 1977) and of few others.