K-theory and the connection index

Let G denote a split simply connected almost simple p-adic group. The classical example is the special linear group SL(n). We study the K-theory of the unramified unitary principal series of G and prove that the rank of K_0 is the connection index f(G). We relate this result to a recent refinement of the Baum-Connes conjecture, and show explicitly how generators of K_0 contribute to the K-theory of the Iwahori C*-algebra I(G).Comment: 11 page

Coincidence points and RR-weakly commuting maps

summary:In this paper we extend the concept of $R$-weak commutativity to the setting of single-valued and multivalued mappings. We also establish a coincidence theorem for pairs of $R$-weakly commuting single-valued and multivalued mappings satisfying a contractive type condition

Some Fixed Point Theorems in -Metric Space Endowed with Graph

We define some notions of contraction mappings in -metric space endowed with a graph and subsequently establish some fixed point results for such classes of contractions. According to the applications of our results, we obtain fixed point theorems for cyclic operators and an existence theorem for the solution of an integral equation

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

An existence theorem for Volterra-type integral inclusion is establish in b-metric spaces. We first introduce two new F-contractions of Hardy–Rogers type and then establish fixed point theorems for these contractions in the setting of b-metric spaces. Finally, we apply our fixed point theorem to prove the existence theorem for Volterra-type integral inclusion. We also provide an example to show that our fixed point theorem is a proper generalization of a recent fixed point theorem by Cosentino et al

Common fixed point theorems for a family of multivalued F-contractions with an application to solve a system of integral equations

Inspired by the work of Wardowski in [33] and Samet et al. in [26], in this article, we introduce some new contractive conditions for sequence of multi functions. We have constructed non-trivial examples to validate our results. We have applied our results to find a solution of a system of integral equations

On Nonlinear Contractions in New Extended -Metric Spaces

Very recently, the notion of extended -metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended -metric space is given

An Approach to Existence of Fixed Points of Generalized Contractive Multivalued Mappings of Integral Type via Admissible Mapping

We investigate the existence of a fixed point of certain contractive multivalued mappings of integral type by using the admissible mapping. Our results generalize the several results on the topic in the literature involving Branciari, and Feng and Liu. We also construct some examples to illustrate our results