It may be observed that though the function φ has been defined in the same way as
the altering distance function, the way it has been used in Theorem 1.4 is completely different
from the use of altering distance function.
Weakly contractive mappings have been dealt with in a number of papers. Some of
these works are noted in 17–20.
The purpose of this paper is to introduce a generalisation of Banach contraction
mapping principle which includes the generalisations noted in Theorems 1.2 and 1.4. Lastly,
we discuss an example.