Sufficient conditions are given for a mapping to be γ -G inverse differentiable. Constrained implicit function theorems for γ -G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed subset. A theorem without assuming the γ -G inverse differentiability in a finite-dimensional space is also presented.

Abstract. Let G = (V,E) be a simple graph. A function f : V → {−1, 1} is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of G, denoted by γ0 st(G), equals to the maximum weight of an inverse signed total dominating function of G. In this paper, we establish upper bounds on...

In this paper, we give a generalized Cline?s formula for the Drazin inverse. Let R be ring, and let a, b, c, d ? satisfying (ac)2 = (db)(ac), (db)2 (ac)(db), b(ac)a b(db)a, c(ac)d c(db)d. Then ac Rd if only bd Rd. case, (bd)d b((ac)d)2d: We also present formulas group inverses. Some weaker conditions in Banach algebra are investigated. These extend main results of on g-Drazin inverse Liao, Chen...

The concept of an inverse of a singular matrix seems to have been first introduced by Moore [1], [2] in 1920. Extensions of these ideas to general operators have been made by Tseng [3], [4], [5], but no systematic study of the subject was made until 1955 when Penrose [6], [7], unaware of the earlier work, redefined the Moore inverse in a slightly different way. About the same time one of the au...

The inverse degree r(G) of a finite graph G = (V,E) is defined as r(G) = ∑ v∈V 1 d(v) , where d(v) is the degree of vertex v. In Discrete Math. 310 (2010), 940-946, Mukwembi posed the following conjecture: Let G be a connected chemical graph with diameter diam(G) and inverse degree r(G). Then diam(G) ≤ 12 5 r(G) +O(1). In this paper, we settle the conjecture affirmatively.

The concept of inverse problems is now a familiar one to most scientists and engineers, particularly in the field of imaging systems and computer vision. Inverse problems arise whenever we want to infer an unknown quantity f(r) which is not directly observable through a measurement system H which gives access to an observable quantity g(s). The mathematical equations linking these two quantitie...