[PDF] Top 20 Best proximity results: optimization by approximate solutions

... find best proximity pairs between two subsets of a met- ric space with a partial ...the best proximity pair (x, Sx) if d(x, Sx) = d(A, ...a best proximity point of S and the ... See full document

... in optimization had a keen interest in approximate solutions of optimization ...of solutions. One of them is that an approximate solution of an optimization problem can be ... See full document

... istence results for solutions of set-valued optimization problems and a generalized vector T-inequality problem under the assumption of cone-convexity for set-valued ...for approximate ... See full document

... colony optimization is a technique for optimization that was introduced in the early ...colony optimization is the foraging behaviour of real ant ...of approximate solutions to discrete ... See full document

... point results, see [–] and refer- ences ...an approximate solution x that is optimal in the sense that the dis- tance d(x, Tx) is ...well-known best approximation theorem, due to Fan [], states ... See full document

... whose solutions are the fixed points of the mapping T : X → X, where X is a nonempty ...no solutions and, in this case, it is of a certain interest to determine an approximate solu- tion x that is ... See full document

... a best proximal point. The setting of best proximity point theory is richer and more general than the metric fixed point theory in two ...best proximity. Secondly, if one takes A = B in ... See full document

... though best approximation theorems ensure the existence of approx- imation solutions, such results need not yield optimal ...But, best proximity point theorems provide sufficient ... See full document

... the best approximation problems and then we obtain the solution which is not opti- mal but is approximate solution to the equation U x = ...these approximate solutions we attain the target to ... See full document

... some best proximity point results using generalized weak contractions with discontinuous control ...optimal approximate solution of a fixed point ...coupled best proximity point ... See full document

... a best proximity point theorem for non-self-mappings satisfied proximal cyclic contraction in PM-spaces and this shows the existence of optimal approximate solutions of certain simultaneous ... See full document

... K best paths algorithm is involved: under an “easier” ...K best paths al- gorithm to generate the candidate trajectories of step (1) ...good solutions under one function has a high likelihood of ... See full document

... some best proximity point theorems for various classes of cyclic contractions by using a geometric notion of monotone proximally property on a nonempty pair of subsets in a metric space equipped with a ... See full document

... the approximate solutions of the equation Sx = ...interesting best proximity point theorems for various classes of non-self mappings in different frameworks and best ap- proximation ... See full document

... a best proximity point of the mapping T iff d(x ∗ , Tx ∗ ) = inf { d(a, b) : a ∈ A, b ∈ B } ...a best proximity point of T will be a fixed point of T ...of best proximity point ... See full document

... For the same operators we have studied in the previous section, we will formulate and prove useing Theorem 2.2, in order to obtain results for diameter approximate best proximity pair. Theorem ... See full document

... Let A be a nonempty subset of a metric space (X, d) and T : A → X. A solution to the equation Tx = x is called a fixed point of T . It is obvious that the condition T(A) ∩ A = ∅ is necessary for the existence of a fixed ... See full document

... Abstract—In this paper, we solve Caputo fractional-order Bloch equations. The Bloch equations are a model for nuclear magnetic resonance (NMR), which is a physical phenomenon arising in engineering, medicine, and the ... See full document

... these results are ...Tx. Best approximation theorems and best proximity point theorems are pertinent in this ...of best proximity ... See full document

... Markins [] and Nadler [] initiated the study of fixed point theorems for set valued opera- tors. Since then, several other papers have been concerned with the study of multi-valued operators in variant (generalized) ... See full document