The Ordered Implicit Relations: Fixed Point Problems and Applications
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.7033Keywords:
fixed point, implicit relationAbstract
We introduce an ordered implicit relation and obtain related fixed point theorems in rectangular cone $b$-metric space, as an extension of the results on cone metric, rectangular cone metric and cone $b$-metric space. We provide some examples as an explanation of established outcomes. Our theorems universalize many fixed point outcomes in literature(\cite{23}, \cite{k6}). An homotopy result as an application of main theorem is given, which further applied to the human aging process. The obtained fixed point results do not follow from the results proved by Ercan \cite{er}, as the present article deals with nonlinear contractions. The convergence of the sequence generated by Urysohn integral operator is also shown by using fixed point technique.
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Copyright (c) 2025 Anam Arif, Muhammad Nazam, Hijaz Ahmad, Ibrahim Alraddadi Alraddadi, Changjin Xu, Waleed Mohammed Abdelfattah
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