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

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 such as $D_d^{\ast }$ -Symmetric spaces and weakly compatible maps are reviewed to establish the framework for our main results. 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 $D_d^{\ast }$ -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 mapping. Additionally, various common fixed point outcomes for the two pairs of self-maps were determined.

This manuscript explores novel outcomes regarding 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 $D_d^{\ast }$ -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 implementations in each advanced branches of science.