Weighted sharing of sets in wider sense under the ambit of higher indexed polynomials

Abstract

In this article, with respect to the recently introduced definition of weighted sharing of sets in the wider sense [8], we have comprehensivelyextended and improved some well known results in the literature. As the definition involves the manipulations of two polynomials, we perceive that the characteristizations of the underlying polynomials become utmost important. This realization urges us to introduce the definition of the index of polynomial. Noting that, in case of weighted sharing of sets the polynomials so far chosen are of lower index, after defining and streamlining the index concept, we explore the influence of using polynomials with higher indices in the context of weighted sharing of sets in wider sense to improve and extend a number of earlier results.