THE MODIFIED PICARD-FB ITERATIVE ALGORITHM FOR APPROXIMATING THE FIXED POINTS OF CONDITIONAL QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES AND ITS RATE OF CONVERGENCE.

In this paper, the new modified Picard-FB iterative algorithm based on the idea of the iterative algorithm of Fukhar-ud-din and Berinde in [H. Fukhar-ud-dina, V. Berinde, Iterative methods for the class of quasicontractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat 30 (2016), 223-230.] is defined. We also introduce the class of conditional quasi-contractive mappings in convex metric spaces and prove the convergence result of the purposed iterative algorithm for approximating the fixed points for conditional quasi-contractive mappings in convex metric spaces. Furthermore, a comparison result of the rate of convergence of the new purposed iterative algorithm, the iterative algorithm of Fukhar-ud-din and Berinde and many iterative algorithms in convex metric spaces is investigated. [ABSTRACT FROM AUTHOR]