‎In this paper‎, ‎we introduce more general contractions called $varphi $-fixed‎ ‎point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $varphi $-‎fixed point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to sup...

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

To any graph G we can associate a simplicial complex ∆(G) whose simplices are the complete subgraphs of G, and thus we say that G is contractible whenever ∆(G) is so. We study the relationship between contractibility and K-nullity of G, where G is called K-null if some iterated clique graph of G is trivial. We show that there are contractible graphs which are not K-null, and that any graph whos...

Consider the equation div$(\varphi^2 \nabla \sigma)=0$ in $\mathbb{R}^N,$ where $\varphi>0$. It is well-known that if there exists $C>0$ such $\int_{B_R}(\varphi \sigma)^2 dx\leq CR^2$ for every $R\geq 1$ then $\sigma$ necessarily constant. In this paper we prove result not true replace $R^2$ by $R^k$ $k>2$ any dimension $N$. This question related to a conjecture De Giorgi.

Abstract Two reduced projective schemes are said to be Cremona equivalent if there is a map that maps one in the other. In this paper I revise some of known results about equivalence and extend main result Mella Polastri (Bull Lond Math Soc 41(1):89–93, 2009) [20] reducible schemes. This allows prove very general contractibility for union rational subvarieties.

Invariants for Riemann surfaces covered by the disc and hyperbolic manifolds in general involving minimizing measure of image over homotopy homology classes closed curves maps k-sphere into manifold are investigated. The invariants monotonic under holomorphic mappings strictly certain circumstances. Applications to annular regions ℂ tubular neighborhoods compact totally real submanifolds n , n≥...