The aim of the paper is to introduce new Suzuki and convex type contractions and prove new best proximity results for these contractions in the setting of a metric space. As applications, we deduce similar results for such type of contractions in partially ordered metric spaces and derive new Suzuki type fixed point results. An illustrative example is provided here to highlight our findings.

The aim of this paper is to introduce and study certain new concepts of α-ψ-proximal contractions in an intuitionistic fuzzy metric space. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered intuitionistic fuzzy metric spaces. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain some recent fixed point theorems as special cases. Moreover, we discuss some illustrative examples to highlight the realized improvements. MSC: 47H10; 54H25

In this paper, first we introduce certain new classes of Suzuki type contractions in triangular and non-Archimedean fuzzy metric spaces. Further we establish fixed point theorems for such kind of mappings in non-Archimedean and triangular fuzzy metric spaces. We also prove Suzuki type fixed point results in non-Archimedean and triangular ordered fuzzy metric spaces. The results presented here improve and generalize certain recent results from the literature. Two illustrative examples and an application to integral equations are given to support the usability of our results. MSC: 46N40; 47H10; 54H25; 46T99

Let M be a module over a commutative ring R. In this paper, we continue our study about the quasi-Zariski topology-graph G(τ * T) which was introduced in (On the graph of modules over commutative rings, Rocky Mountain J. Math. 46(3) (2016), 1-19). For a non-empty subset T of Spec(M), we obtain useful characterizations for those modules M for which G(τ * T) is a bipartite graph. Also, we prove that if G(τ * T) is a tree, then G(τ * T) is a star graph. Moreover, we study coloring of quasi-Zariski topology-graphs and investigate the interplay between χ(G(τ * T)) and ω(G(τ * T)).

In this paper, we introduce the concept of grey [Formula: see text]-acts and morphisms between grey [Formula: see text]-acts on monoids, which construct a category, namely, [Formula: see text]. Next, we define indecomposable, cyclic, free and projective grey [Formula: see text]-acts. We show that any grey [Formula: see text]-act is a free grey [Formula: see text]-act if and only if it is a free object in this category. Also, we show that any grey [Formula: see text]-act is epimorphism image of any free grey [Formula: see text]-act. We prove that any free grey [Formula: see text]-act is a projective grey [Formula: see text]-act and any cyclic grey [Formula: see text]-act is an indecomposable grey [Formula: see text]-act.