θ*-Weak Contractions and Discontinuity at the Fixed Point with Applications to Matrix and Integral Equations

In this paper, the notion of θ*-weak contraction is introduced, which utilized to prove some fixed point results. These results are helpful give a positive response certain open question raised by Kannan and Rhoades on existence contractive definition does not force mapping be continuous at point. Some illustrative examples also given support our As applications result, we investigate uniqueness solution non-linear matrix equations integral Volterra type as well.