We analyze Greedy Mapping, a simple mapping method that has successfully been used on mobile robots. Greedy Mapping moves the robot from its current location on a shortest path towards a closest unvisited, unscanned or informative location, until the terrain is mapped. Previous work has resulted in upper and lower bounds on its worst-case travel distance but there was a large gap between the bo...

The alternating direction method is an attractive method for a class of variational inequality problems if the subproblems can be solved efficiently. However, solving the subproblems exactly is expensive even when the subproblem is strongly monotone or linear. To overcome this disadvantage, this paper develops a new alternating direction method for cocoercive nonlinear variational inequality pr...

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of finite generalized Ky Fan inequalities and the set of solutions of more general variational inequality for finite relaxed cocoercive operators and the set of common fixed points of a nonexpansive semigroup in Hilbert space. The results obtained in this paper improve and extend the resul...

We introduce a new iterative scheme by modifying Mann’s iteration method to find a common element for the set of common fixed points of an infinite family of asymptotically strictly pseudocontractive mappings in the intermediate sense, the set of solutions of the cocoercive quasivariational inclusions problems, and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The st...

In this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On xed-point the- orems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252].

Abstract Splitting algorithms for finding a zero of sum operators often involve multiple steps which are referred to as forward or backward steps. Forward the explicit use and implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm three operators. We assume that two generalized monotone resolvents computable, while other operator is cocoercive but its resolvent...