Weak θ-φ-contraction and discontinuity.

In this paper, we introduce the notion of weak Weak θ-φ-contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233-245]. [ABSTRACT FROM AUTHOR]