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Common fixed points and invariant approximation for Gregus type contraction map**s

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Abstract

Some new common fixed point theorems for Gregus type contraction map**s have been obtained in convex metric spaces. As applications, invariant approximation results for these types of map**s 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. Ćirić (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.

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  1. Department of Mathematics, Guru Nanak Dev University, Amritsar, 143005, India

    Sumit Chandok & T. D. Narang

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  1. Sumit Chandok
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  2. T. D. Narang
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Chandok, S., Narang, T.D. Common fixed points and invariant approximation for Gregus type contraction map**s. Rend. Circ. Mat. Palermo 60, 203–214 (2011). https://doi.org/10.1007/s12215-011-0043-5

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