New generalized Trends of Coupled Fixed Point Theorems for Continuous Mappings Satisfying a Property of Mixed Monotone

<ns3:p>Background One of the most important results of mathematical analysis is the Banach fixed point theory, he explained in this theory that a mapping T: X → X always has a unique fixed point in X. After witnessing the implementations of this theory in giving the existence and uniqueness solutions for many integral and differential equations, additionally discovery of solutions for linear and nonlinear systems, various extensions of this theory were carried out. Our main results represent one of the most important of these generalizations in the literature. Methods and Results Various vital concepts are needed in the sequels which are playing a major role in verifying our major outcomes have been presented. Throughout this manuscript, ( X , ≼ ) indicates to a partially ordered set with the partially ordered ≼ . In this study, our main objective is to investigate and verify various new enhanced results of coupled fixed point theorems for continuous maps having the property of mixed monotone under the influence of extended contraction circumstances in the context of partially ordered D ∗ -complete metric spaces. Numerous characterizations of these types of coupled fixed point theorems have been verified. Our major outcomes are extending and enhancing the various outcomes of coupled fixed point theorems existing in the literature. Additionally, an appropriate example that supports the major outcomes was prepared. Conclusions Our main results in this manuscript have been explored novel various outcomes related to the uniqueness of various coupled fixed point theorems for continuous maps having the property of mixed monotone under the influence of extended contraction circumstances in the context of partially ordered D ∗ -complete metric spaces. We predict that the discoveries in this study will aid scientists in enhancing the research on popularized partially ordered metric spaces to elevate a universal framework for their practical implementations.</ns3:p>