Lacunary series expansions in hyperholomorphic \(F^{\alpha}_{G}(p,q,s)\) spaces

Abstract

In this paper we define a new class of hyperholomorphic functions, which is known as F α G (p, q, s) spaces. We characterize hyperholomorphic functions in F α G (p, q, s) space in terms of the Hadamard gap in Quaternion analysis.

Cannabinoid Receptor 2 (CB2) Signals via G-alpha-s and Induces IL-6 and IL-10 Cytokine Secretion in Human Primary Leukocytes

“…As this was completely sensitive to both Gβγ inhibitor gallein and Gαi/o/βγ inhibitor PTX, we conclude that ERK1/2 phosphorylation induced by HU308 is mediated by βγ dimers of Gαiβγ heterotrimeric proteins. Although in some systems gallein may inhibit GRK2 and possibly associated arrestin signaling 73 , we do not know of any studies suggesting that PTX blocks arrestin-initiated signaling other than one report of a small potency shift for arrestin recruitment 74 . Interestingly NF023, which we confirmed in cAMP assays inhibits Gαi, did not block the p-ERK response, indicating that this blocker specifically inhibits Gα subunits without influencing Gβγ activity as also observed previously 75 In contrast with prior studies in human promyelocytic leukemia HL60 cells 25 and CB2overexpressing HEK cells 24 we did not observe JNK phosphorylation.…”

Certain subclasses of analytic functions associated with Mittag–Leffler-type Poisson distribution series

“…Motivated by results on connections between various subclasses of analytic univalent functions using hyper-geometric functions [7,16], generalized Bessel functions [15], Poisson distribution series [2,8,12], hyper-geometric distribution series [1], confluent hyper-geometric distribution series [17], Binomial distribution series [9] and generalized distribution series [13] also one can refer [2, 6, 8, 10-14, 16, 19, 20] and the references there in this paper we obtain some necessary and sufficient conditions for Kðm; a; bÞ and Kðm; a; b; f Þ belong to the class Kðk; dÞ.…”