Abstract Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of problem at hand replaced by Hamming distance a given solution, and cutoff constraint added impose that any new obtained solution improves value. A mixed integer solver used find feasible this modified problem, yielding improved original problem. This ...

in this paper, based in the l ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.

In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.

In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.