Some Extended Results of Common Fixed Point Theorems via Enhanced Categories of Contractive Mappings in Dd* - Symmetric Spaces

<ns3:p>Background The Banach fixed point theory stated 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, various extensions of Banach fixed point theory were carried out. Therefore, fixed point theory has been developed and diversified to encompass various 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. Methods and Results Various vital concepts such as ( D d ∗ -Symmetric and weakly compatible maps) that are needed in the sequel, which will help us in the outcomes that follow and play a major role in verifying our major outcomes. The major objective of the present study is to investigate and verify the uniqueness of some common fixed point theorems for three pairs of self-maps under the influence of other enhanced categories of extended contractive conditions in the context of D d ∗ -Symmetric spaces. Our first main outcomes were established by applying the concepts of weak compatibility and common limit in the range property, whereas we obtained our second major results by utilizing the notion of occasionally weakly compatible (Concisely, O.W.C) maps that are more general than weakly compatible. Additionally, various common fixed point outcomes for the two pairs of self-maps were determined. Conclusion Our main results in this manuscript have been explored novel various outcomes related to the uniqueness of various common fixed point theorems for three pairs of self-maps under the influence of other enhanced types of extended contractive conditions in the context of D d ∗ -Symmetric spaces. We anticipate that the discoveries in this manuscript will aid scientists in enhancing the authors on popularized extended symmetric-spaces to elevate a universal framework for their practical implementation in each advanced branches of science.</ns3:p>