This paper deals with the existence of an optimum solution a system ordinary differential equations via best proximity points. In order to obtain solution, we have developed point results for generalized multivalued contractions b-metric spaces. Examples are given illustrate main and show that new proper generalization some existing in literature.

In this paper we present a novel approximate algorithm to calculate the top-k closest pairs join query of two large and high dimensional data sets. The algorithm has worst case time complexity OðdnkÞ and space complexity OðndÞ and guarantees a solution within a Oðd1þ1tÞ factor of the exact one, where t 2 {1,2, . . . ,1} denotes the Minkowski metrics Lt of interest and d the dimensionality. It m...

The aim of the paper is to show the validity of results of Imdad [7] in a domain which is not necessarily starshaped and mappings are not necessarily linear. Our results also improve, extend and generalize various existing known results in the literature.