R-groups and geometric structure in the representation theory of SL(N)

Let F be a nonarchimedean local field of characteristic zero and let G = SL(N) = SL(N,F). This article is devoted to studying the influence of the elliptic representations of SL(N) on the K-theory. We provide full arithmetic details. This study reveals an intricate geometric structure. One point of interest is that the R-group is realized as an isotropy group. Our results illustrate, in a special case, part (3) of the recent conjecture in [2]. <br/

Best coapproximation in L∞(µ, X)

Let X be a real Banach space and let G be a closed subset of X. The set G is called coproximinal in X if for each x ∈ X, there exists y₀ ∈ G such that ||y − y₀|| ≤ ||x – y|| , for all y ∈ G. In this paper, we study coproximinality of L∞(µ, G) in L∞(µ, X), when G is either separable or reflexive coproximinal subspace of X.Publisher's Versio

On solutions of differential and integral equations using new fixed point results in cone Eb-metric spaces

The focus of this study is to establish the existence and uniqueness of solutions for differential and integral equations within specific metric spaces. Our investigation begins by introducing the concept of the so-called cone Eb-metric space and presenting crucial findings in this particular space. We have presented fixed point results for specific contractions, particularly in the context of non-solid cones that possess semi-interior points. Not only do the results enhance specific previous fixed points outcomes, but they also encompass and extend previous findings documented in the literature. Furthermore, we apply our findings in the cone Eb-metric space to various examples and applications. The ultimate outcome is the rigorous validation of the existence and uniqueness of solutions for certain differential and integral equations