Abstract:
Metric Fixed Point Theorems for Single-valued and Multi-valued
Mappings
The main goal of the present research is to establish existence and uniqueness theorems
regarding fixed points, coincidence points and common fixed points of single-valued and
multi-valued mappings in connection with contractive type inequalities in complete
metric spaces and generalized metric spaces. Some notions namely generalized α*-
Mizoguchi-Takahashi type contraction, generalized Mizoguchi-Takahashi G contraction
and α-admissible mappings for cone metric space are also obtained. We also include an
application in which we prove the existence and uniqueness of a solution for a general
class of Fredholm integral equation of 2nd kind. To enhance the validity of this work
some interesting examples are also furnished.
