In this paper, we introduce a new class of fuzzy contractive mappings under the name of ‘ ( F Z , F , φ ) -contractive mappings’ and utilize the same to prove fuzzy φ -fixed point results. Some illustrative examples are also given to support our results besides deriving several consequences. As an application, we prove an existence and uniqueness result on the solution of first order periodic differential equation. Interestingly, this newly introduced class unifies several known contractions such as: fuzzy contractive, fuzzy ψ -contractive, fuzzy H -contractive and fuzzy F Z -contractive mappings.

In this paper, we introduce the notions of (F,$\phi$,$\alpha$-$\psi$)-contractions and (F,$\phi$,$\alpha$-$\psi$)-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness $\phi$-fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature.

In this manuscript, we introduce the notions of various types of ${\mathsf{\Theta }}_c$-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings, which generalize many results of invariance and transformations in the literature.

In this paper, we establish some point of φ-coincidence and common φ-fixed point results for two self-mappings defined on a metric space via extended CG-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations.

In this paper, we introduce the notion of generalizedL-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion ofL∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.

In this article, we introduce and study a novel class of polynomial $\phi$-contractions, which simultaneously generalizes classical polynomial contractions and $\phi$-contractions within a unified framework. We establish generalized fixed point theorems that encompass some results in the existing literature. Furthermore, we derive explicit error estimates and convergence rates for the associated Picard iteration, providing practical insights into the speed of convergence. Several illustrative examples, including higher-degree polynomial contractions, demonstrate the scope and applicability of our results. As an application, we prove existence and uniqueness results for solutions of a class of fractional logistic growth equations, highlighting the relevance of our theoretical contributions to nonlinear analysis and applied mathematics.