Abstract
In this paper, we firstly propose the notion of double controlled partial metric type spaces, which is a generalization of controlled metric type spaces, partial metric spaces, and double controlled metric type spaces. Secondly, our aim is to study the existence of fixed points for Kannan type contractions in the context of double controlled partial metric type spaces. The proposed results enrich, theorize, and sharpen a multitude of pioneer results in the context of metric fixed point theory. Additionally, we provide numerical examples to illustrate the essence of our obtained theoretical results.
Highlights
Introduction and Preliminaries e study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been at the middle of vigorous research activity
Banach contraction mapping principle has attracted the eye of the many authors to generalize, extend, and improve the metric fixed point theory
It is useful to establish the extensions of the contraction principle from metric spaces to b-metric spaces, and the controlled metric type of spaces is useful to prove the existence and uniqueness of theorems for many forms of integral and differential equations
Summary
Introduction andPreliminaries e study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been at the middle of vigorous research activity. Many researchers worked on the partial metric type spaces to discover the existence of fixed point and their uniqueness. (1) d(x1, x2) 0 if and only if x1 x2, (2) d(x1, x2) d(x2, x1), (3) d(x1, x1) ≤ d(x1, x2), (4) d(x1, x2) ≤ α(x1, x3)d(x1, x3) + μ(x3, x2)d(x3, x2), for all x1, x2, x3 ∈ X, (X, d) is called a double controlled partial metric type space.
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