Yaying, TajaHazarika, BipanIlkhan, MerveMursaleen, M.2021-12-012021-12-0120210139-99181337-2211https://doi.org/10.1515/ms-2021-0048https://hdl.handle.net/20.500.12684/10920The incomplete gamma function (a, u) is defined by Gamma(a, u) = integral(infinity)(u) t(a-1)e(-t) dt, where u > 0. Using the incomplete gamma function, we define a new Poisson like regular matrix beta(mu) = (p(nk)(mu)) given by p(nk)(mu) = {n!/Gamma(n+1, mu) e(-mu)mu(k)/k! (0 <= k <= n), 0 (k > n), where mu > 0 is fixed. We introduce the sequence space l(p) (beta(mu)) for 1 <= p <= 1 and some topological properties, inclusion relations and generalized duals of the newly defined space are discussed. Also we characterize certain matrix classes and compact operators related to the space l(p) (beta(mu)). We obtain Gurarii's modulus of convexity and investigate some geometric properties of the new space. Finally, spectrum of the operator beta(mu) on sequence space c(0) has been investigated. (C) 2021 Mathematical Institute Slovak Academy of Sciencesen10.1515/ms-2021-0048info:eu-repo/semantics/closedAccessPoisson matrixincomplete gamma functionmatrix transformationscompact operatorsgeometric propertiesspectrum of matrix operatorBinomial Difference OperatorEuler Sequence-SpacesHausdorff MeasureCompactnessNoncompactnessIncludeL(P)Article715118912102-s2.0-85117963627WOS:000704587300011Q2Q2