Common fixed points for multivalued generalized contractions on partial metric spaces

Abstract

We establish some common fixed point results for multivalued mappings satisfying generalized contractive conditions on a complete partial metric space. The presented theorems extend some known results to partial metric spaces. We motivate our results by some given examples and an application for finding the solution of a functional equation arising in dynamic programming.

Common fixed point results of generalized almost rational contraction mappings with an application

“…The existence and uniqueness of solutions of functional equations and system of functional equations arising in dynamic programming have been studied by using different fixed point results (see, [1,7,22,30]). …”

“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”

A general fixed point theorem for a pair of multi-valued mappings in partial metric spaces

“…Continuing in this manner, we can construct a sequence {x n } in X such that (4) x 2n+1 ∈ Sx 2n and x 2n+2 ∈ T x 2n+1…”

“…The purpose of this paper is to prove a general fixed point theorem for a pair of multi-valued mappings satisfying a new type of implicit relation in partial metric spaces, which generalizes Theorems 2.2 [4], Theorem 3.1 [3], Theorem 3.2 [7], Corollary 2.3 [4], Theorem 2.8 [16] and obtain other particular results.…”

“…Quite recently, in [4] is proved a common fixed point theorem for a pair of multi-valued mappings satisfying a contractive condition in partial metric spaces.…”