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.

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In this paper, we introduce the notions of (F,ϕ,α-ψ)-contractions and (F,ϕ,α-ψ)-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness ϕ-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 paper, we begin with some observations on F-contractions. Thereafter, we introduce the notion of (F, R) g-contractions and utilize the same to prove some coincidence and common fixed point results in the setting of metric spaces endowed with binary relations. An example is also given to exhibit the utility of our results. We also deduce some consequences in the setting of ordered metric spaces. As an application, we investigate the existence and uniqueness of a solution of integral equation of Volterra type.

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