Some New Fixed Point Theorems in Weak Partial Metric Spaces

Abstract

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions (ψ − φ)in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

Dismountable and non-Dismountable Spaces via Proximity Space

“…Others tried to employ the proximity space in another direction, which is creating new sets and constructing set theory (𝜎−𝐴𝑙𝑔𝑒𝑏𝑟𝑎) and then a topological space based on those sets [6][7][8][9] . Other contemporary researchers tried to enrich this space with many interesting concepts [10][11][12][13] .…”

Fixed point on almost generalized (α, ψ, φ, ϑ)-contractive type mappings in weak partial metric spaces

“…The concept of weak partial metric spaces, a generalisation of partial metric spaces, was first introduced by Heckmann [14] in 1999. Some results for mappings in weak partial metric spaces have recently been obtained in [17], [18], [19] and [20]. Definition 1.1.…”