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

After witnessing the implementations of Banach fixed point theory which is stated that a mapping T: X→X has always a unique fixed point in X in giving the existence and uniqueness solutions for many integral and differential equations, various extensions of Banach fixed point theory were established. Consequently, the theory has evolved to encompass diverse extensions and is fruitful in many fields. One of the most significant advances in pure and applied mathematics is the discovery of solutions for linear and nonlinear systems as well fractal graphics, optimization theory, approximation theory, discrete dynamics, and numerous other areas. Our main outcomes in this manuscript represent one of the most important of these extensions.

Vital concepts are needed in the sequels which are playing a major role in verifying our major outcomes have been presented. Throughout this manuscript, $(X,\preccurlyeq )$ indicates to a partially ordered set with the partially ordered $\preccurlyeq$ . 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 $D^{\ast }$ -complete metric spaces. Numerous characterizations of these types of coupled fixed point theorems have been verified. Additionally, an appropriate example that supports the major outcomes was prepared.

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 $D^{\ast }$ -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.