We establish a fixed point theorem for Cirić contraction in the context of convex b-metric spaces. Furthermore, we ensure that there is a fixed point for the maps satisfying the condition (B) (a kind of almost contraction ) in convex b-metric spaces and demonstrate its uniqueness as well. Supporting examples to substantiate the generality of the proved results are given.

In this study, PPF dependent fixed point theorems are proved for a nonlinear operator, where the domain space $C[[a, b], E]$ is distinct from the range space, $E$, which is a Strong Partial b-metric space (SPbMS). We obtain existence and uniqueness of PPF dependent fixed point results for the defined mappings under SPbMS. Our results are the extension of fixed point results in SPbMS. Examples are provided in the support of results.

We present a significant example to show that the class of v-generalized b-metric spaces properly contains the class of v-generalized metric spaces as well as b-metric spaces. This is accomplished because the example provided by Došenović et al. (2020) is insufficient to expose the generality of v-generalized b-metric spaces over the existing related spaces. Therefore, we establish fixed point theorems by defining generalized almost contractions of rational type and Reich type in v-generalized b-metric spaces. Moreover, we compare the proven results with the already existing fixed point theorems in this space by presenting suitable examples. As a consequence of these fixed point theorems, we further develop some common fixed-point results that ensure the existence and uniqueness of coincidence points and common fixed points for a pair of self maps. Finally, we use the outcome to check that the given Fredholm integral equation has a solution and that it is also unique.

In this paper, some results concerning the existence and uniqueness of triple invariant point with PPF dependence for non linear mapping in partially ordered complete metric spaces using the domain space C [[a, b], E] that is distinct from the range E. Our results generalize and extend recent coupled invariant point theorems with PPF dependence founded by Drici et al. (Fixed point theorems in partially ordered metric spaces for operators with PPF dependence, Nonlinear Analysis 67 (2007), 641 -647).

In this paper, we prove fixed point results for various cyclic contractions in partial symmetric spaces. Our results generalize the fixed point results of Asim et al. (Fixed point results in partial symmetric spaces with an application, Axioms 8(13) (2019), 1 -15) proved for the class of partial symmetric spaces for various contractions. Also, we provide an example in the support of proved result.