A transitive triple, (a, b, e), is defined to be the set {(a, b), (b, e), (a, en of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D, (3), where D is a set of v points and (3 is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of (3. An antiautomorphism o...

‎in this paper‎, ‎we construct a new iterative method for solving nonlinear volterra integral equation of second kind‎, ‎by approximating the legendre polynomial basis‎. ‎error analysis is worked using banach fixed point theorem‎. ‎we compute the approximate solution without using numerical method‎. ‎finally‎, ‎some examples are given to compare the results with some of the existing methods‎.

In this paper we introduce the concept of generalized weakly contractiveness for a pair of multivalued mappings in a metric space. We then prove the existence of a common fixed point for such mappings in a complete metric space. Our result generalizes the corresponding results for single valued mappings proved by Zhang and Song [14], as well as those proved by D. Doric [4].

In this paper, we investigate a new type of random $F$-contraction and obtain a common random fixed point theorem for a pair of self stochastic mappings in a separable Banach space. The existence of a unique solution for nonlinear fractional random differential equation is proved under suitable conditions.

In our recent research we studied a feasibility problem with infinitely many sets in metric space, presented novel algorithm and analyzed its convergence. the present paper study introduced that work for common fixed taking into account computational errors. We show generates good approximate solution, if errors are bounded from above by small positive constant.