We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

This paper is a contribution to the theory of substructural logics. We introduce the notions of (MP)-based and almost (MP)-based logics (w.r.t. a special set of formulae D), which leads to an alternative proof of the well-known forms of the local deduction theorems for prominent substructural logics (FL, FLe, FLew , etc.). Roughly speaking, we decompose the proof of the local deduction theorem ...

We consider the nonselfadjoint Sturm-Liouville operator with regular but not strongly regular boundary conditions. We examine the basis property of the root function system of the mentioned operator. In the present paper we study eigenvalue problems for the nonselfadjoint Sturm-Liouville operator Lu = u′′ − q(x)u (1) defined on the interval (0, 1), where q(x) is an arbitrary complex-valued func...

α-Helices are the most abundant structures found within proteins and play an important role in the determination of the global structure of proteins and their function. Representation of α-helical structures with the common (φ, ψ) dihedrals, as in Ramachandran maps, does not provide informative details regarding the helical structure apart for the abstract geometric meaning of the dihedrals. We...