In this paper, we introduce a new concept of partial rectangular metric-like space and prove some results on the existence and uniqueness of a fixed point of a function
T
:
X
⟶
X
, defined on a partial rectangular metric-like space
X
, which fulfills a nonlinear contractive condition using a comparison function and the diameter of the orbits. The obtained results generalize some previously acknowledged results in partial metric spaces, partial rectangular metric spaces, and rectangular metric-like spaces. The examples presented prove the usefulness of the introduced generalizations.
In this paper we prove some conditions for equivalent Cauchy sequences in partial metric spaces. These conditions are necessary and sufficient for 0-equivalent 0-Cauchy sequences in partial metric spaces. Some examples are given to illustrate the observed results.
In this paper we will define the new weighted statistically summbaility method, known as the weighted Norlund-Euler statistical convergence. We will show some properties of this method and we have proved Korovkin type theorem.
Mathematics Subject Classification: 40G15
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