Weakly Picard pairs of multifunctions

Valeriu Popa

doi:10.4067/S0719-06462010000100006

Authors

Valeriu Popa Department of Mathematics, University of BacÄƒu, Str. Spiru Haret nr. 8, 600114 BacÄƒu, Romania.

DOI:

https://doi.org/10.4067/S0719-06462010000100006

Keywords:

Multifunction, fixed point, implicit relation, weakly Picard multifunction, weakly Picard pair of multifunctions

Abstract

The purpose of this paper is to present a general answer for the following problem: Let (X, d) be a metric space and T₁, T₂ : X â†’ P(X) two multifunctions. Determine the metric conditions which imply that (T₁, T₂) is a weakly Picard pair of multifunctions and T₁, T₂ are weakly Picard multifunctions , for multifunctions satisfying an implicit contractive condition, generalizing some results from [6] and [7].