‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

‎Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces‎, ‎and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$‎. ‎We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ ‎related to these grills, and present a simple proof to this theorem‎. ‎This immediately yields the classical theorem...

In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...