In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some known results in the literature. We give examples to analyze and support our main results.

In this paper we give some applications to integral equations as well as homotopy theory via fixed point theorems in partially ordered complete \(S_{b}\)-metric spaces by using generalized contractive conditions. We also furnish an example which supports our main result.

We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order ⪯. This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann ...

We present the random version in partially ordered metric spaces of the classical Banach contraction principle and some of its generalizations to ordered metric spaces. The results are used to prove the existence of solutions for random differential equations with boundary conditions.