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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]

Recently, Asadi et al. [M. Asadi, E. Karapinar, P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, Journal of Inequalities and Applications, 18 (2014)] introduced and studied the concept of an M-metric space and proved Banach and Kannan fixed point results in complete M-metric spaces. In this work, we establish some fixed point results for nonlinear contractive mappings by utilizing the control functions which were initiated by Sintunavarat et al. [W. Sintunavarat, Y. J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Computers and Mathematics with Applications, 62 (2011) 1969-1978]. Presented theorems extend and generalize many existing results in the literature. We also give some illustrative examples. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce notions of a modification of the common limit in the range property and two generalized multi-valued F-contraction mappings in metric spaces. Fixed point results with two concepts mentioned above are established. Also, we give an example to illustrate our main results. As applications, we prove the existence of a common solution for the system of functional equations in dynamic programming. [ABSTRACT FROM AUTHOR]

The purpose of this work is to introduce the new contractive condition which involves mw-distances in metric spaces. The fixed point theorems for mappings satisfying such contractive condition are established via the idea of an adapting-ceiling distance. Two illustrative examples are also given to confirm that our results rightly generalize many results in the literatures. As an application, the existence and uniqueness of the solution for nonlinear Fredholm integral equations and nonlinear Volterra integral equations are investigated via our main result. [ABSTRACT FROM AUTHOR]