Abstract
In this manuscript, we introduce the concept of complex-valued triple controlled metric spaces as an extension of rectangular metric type spaces. To validate our hypotheses and to show the usability of the Banach and Kannan fixed point results discussed herein, we present an application on Fredholm-type integral equations and an application on higher degree polynomial equations.
Highlights
Since the breakthrough of Banach [1] in 1922, where he was able to show that a contractive mapping on a complete metric space has a unique fixed point, the field of fixed point theory has become an important research focus in the field of mathematics; see [2,3,4,5,6]
Due to the fact that fixed point theory has many applications in many fields of science, many researchers have been working on generalizing his result by either generalizing the type of contractions [7,8,9,10] or by extending the metric space itself (b-metric spaces [11, 12], controlled metric spaces [13], double controlled metric spaces [14], etc.)
Going in the same direction, recently, Ullah et al [17] presented complex-valued extended b-metric spaces to extend the idea of extended b-metric spaces
Summary
Since the breakthrough of Banach [1] in 1922, where he was able to show that a contractive mapping on a complete metric space has a unique fixed point, the field of fixed point theory has become an important research focus in the field of mathematics; see [2,3,4,5,6]. Due to the fact that fixed point theory has many applications in many fields of science, many researchers have been working on generalizing his result by either generalizing the type of contractions [7,8,9,10] or by extending the metric space itself (b-metric spaces [11, 12], controlled metric spaces [13], double controlled metric spaces [14], etc.). Going in the same direction, recently, Ullah et al [17] presented complex-valued extended b-metric spaces to extend the idea of extended b-metric spaces In this manuscript, following the path of the work done in [18], we extend complex-valued rectangular extended b -metric spaces [19] to complex-valued triple controlled metric spaces.
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