Exciting Fixed Point Results on a Novel Space with Supportive Applications
Hasanen A. Hammad, Hassen Aydi, Yaé Ulrich Gaba
Abstract
The goal of this paper is to present a new space, a complex valued controlled rectangular <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>b</a:mi> </a:math> -metric space (for short, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:msub> <c:mrow> <c:mi>υ</c:mi> </c:mrow> <c:mrow> <c:mi>ℂ</c:mi> </c:mrow> </c:msub> </c:math> -metric space). Some examples and topological properties of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:msub> <e:mrow> <e:mi>υ</e:mi> </e:mrow> <e:mrow> <e:mi>ℂ</e:mi> </e:mrow> </e:msub> </e:math> -metric spaces are given. Also, some related common fixed point results are discussed. Our results generalize a lot of works in this direction. Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. Finally, a numerical example to find the current that passes through the RLC circuit is illustrated.