In 2001, Brualdi and Hollingsworth proved that an edge-colored balanced complete bipartite graph Kn,n with a color set C = {1, 2, 3, . . . , 2n − 1} has a heterochromatic spanning tree if the number of edges colored with colors in R is more than |R|/4 for any non-empty subset R ⊆ C, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors, namely, any color appe...

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

In this paper, we prove some multivalued Caristi type fixed point theorems. These results generalize the corresponding generalized Caristi’s fixed point theorems due to Kada-Suzuki-Takahashi (1996), Bae (2003), Suzuki (2005), Khamsi (2008) and others. 2000 Mathematics Subject Classification: 47H09, 54H25.

In this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. Next, we investigate some properties of such rings. We prove that $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

where E∗ denotes the dual space of E and 〈·, ·〉 denotes the generalized duality pairing. If E∗ is strictly convex, then J is single valued. In the sequel, we will denote the single-value duality mapping by j. Let C be a nonempty closed convex subset of E. Recall that a self-mapping f : C → C is said to be a contraction if there exists a constant δ ∈ 0, 1 such that ∥f x − f y ∥∥ ≤ δ‖x − y‖, ∀x, ...

Interpolative Kannan contractions are a refinement of contraction, which is considered as one the significant notions in fixed point theory. Gb-metric spaces generalized concept both concepts b-metric and G-metric therefore, common results contraction based on this resultsfor concepts. The purpose manuscript, to take advantage interpolative together with notion Ωb equipped H simulation function...

In the present paper, we introduced concept of generalized multi-valued contraction mappings, via class functions \(\Phi\) and \(\Psi\) Also proved some fixed point results for (\(\phi\),\(\mathfrak{F}\))- mappings on cone b-metric spaces over Banach algebra \(\mathfrak{V}\). The conditions existence uniqueness are investigated. We give an example to support our main result.

Four extended generalized hexagons related to the simple groups G2(2)', PSU4(3), HJ and Suz are characterized by the condition that any triple of points {x, y, z) is a clique of the point graph not in a circle of the extended hexagon if and only if the distance of y and z in the residue at x is 3.