In this paper, we define weak θ-contractions on a metric space into itself by extending θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014 ) and utilize the same to prove some fixed point results besides proving some relation-theoretic fixed point results in generalized metric spaces. Moreover, we give some applications to fractal theory improving the classical Hutchinson–Barnsley′s theory of iterated function systems. We also give illustrative examples to exhibit the utility of our results.

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.

Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications

In this paper, we introduce the notion of fuzzy $\mathcal{R}-\psi -$contractive mappings and prove some relevant results on the existence and uniqueness of fixed points for this type of mappings in the setting of non-Archimedean fuzzy metric spaces. Several illustrative examples are also given to support our newly proven results. Furthermore, we apply our main results to prove the existence and uniqueness of a solution for Caputo fractional differential equations.