In this paper, we introduce the concept of $M_{\nu}$M ν -metric as a generalization of M-metric and ν-generalized metric and also prove an analogue of Banach contraction principle in an $M_{\nu}$M ν -metric space. Also, we adopt an example to highlight the utility of our main result which extends and improves the corresponding relevant results of the existing literature. Finally, we use our main result to examine the existence and uniqueness of solution for a Fredholm integral equation.

In this paper, we enlarge the class of $C^{*}$-algebra valued partial metric spaces as well as the class of $C^{*}$-algebra valued b-metric spaces by introducing the class of $C^{*}$-algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations.

In this paper, we first introduce the class of partial symmetric spaces and then prove some fixed point theorems in such spaces. We use one of the our main results to examine the existence and uniqueness of a solution for a system of Fredholm integral equations. Furthermore, we introduce an analogue of the Hausdorff metric in the context of partial symmetric spaces and utilize the same to prove an analogue of the Nadler contraction principle in such spaces. Our results extend and improve many results in the existing literature. We also give some examples exhibiting the utility of our newly established results.

In this paper, we enlarge the classes of rectangular $M_b$ -metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular $M_{r\xi }$ -metric spaces and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of solution for a system of Fredholm integral equation.

In the present paper, we established multivalued fixed point results on C^*-algebra valued metric spaces and utilized the same to prove fixed point results via Suzuki type contraction. An example is also given to exhibit the utility of our main result. We also provided a system of Fredholm integral equations to examine the existence and uniqueness of solutions supporting our main result.

In this paper, we consider F𝓡-generalized contractivity condition and utilized the same to establish some fixed point results for a self-mapping in partial metric spaces endowed with an amorphous binary relation. Our results generalize several core results of the existing literature. We also furnish some examples to exhibit the utility of our results. Finally, we further deduce fixed point result for cyclic contractions in partial metric spaces.