Fixed points of operators satisfying various contractive conditions in complete partial metric spaces

Abstract

In this paper, we give a generalized definition of diameter of a set in a partial metric space and as a consequence, a Cantor's Intersection like Theorem for partial metric spaces follows. We apply this theorem to study some fixed point results for generalized contractive type mappings over a complete partial metric space and also give some results on continuity of fixed points and simultaneous fixed point.

Cantor's intersection theorem and some generalized fixed point theorems over a locally convex topological vector space

“…In this section following the literatures [2], [5], [8], [10], [12], [14] and [15] we dene Reich-type contractive mapping, Caccioppoli-type contractive mapping, T - Reich-type contractive mapping and T - Caccioppoli-type contractive mapping over a locally convex TVS and with these mappings we have been able to prove some xed point theorems and common xed point theorems over it. Denition 4.1.…”