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One of the interesting questions concerning the stability problems of functional equations is as follows: when is it true that a mapping satisfying a functional equation approximately must be close to the solution of the given functional equation? Such an idea was suggested in 1940 by Ulam 1 . The case of approximately additive mappings was solved by Hyers… (More)

- RIGOBERTO MEDINA
- 2002

We derive explicit stability conditions for delay difference equations in C n (the set of n complex vectors) and estimates for the size of the solutions are derived. Applications to partial difference equations, which model diffusion and reaction processes, are given. 1. Introduction. Stability of systems of difference equations with delays has been… (More)

A class of discrete-time Cohen-Grossberg neural networkswith delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the… (More)

- Rigoberto Medina, Mihály Pituk
- Appl. Math. Lett.
- 2009

- Yilmaz Simsek, Ismail Naci Cangul, Veli Kurt, Daeyeoul Kim, Rigoberto Medina
- 2008

The main purpose of this paper is to study generating functions of the q-Genocchi numbers and polynomials. We prove a new relation for the generalized q-Genocchi numbers, which is related to the q-Genocchi numbers and q-Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define q-Genocchi zeta and… (More)

whose discretization, by means of a difference scheme and a quadrature rule 2 , leads to a particular kind of nonlinear system of equations. Solving it by means of a fixed-point FP iteration process, we noted that such a procedure seems to globally converge, that is, it converges independently of the choice of the starting point. Our aim, here, is to… (More)

- Rigoberto Medina
- 2008

We establish a general form of sum-difference inequality in two variables, which includes both two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to… (More)

1 College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Key Laboratory of Network Control and Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China 3 College of Applied Sciences, Beijing University of Technology, Beijing… (More)

- Rigoberto Medina
- IMA J. Math. Control & Information
- 2008

The stabilization problem of dynamical systems has been discussed by many authors (e.g. Brockett & Liberzon, 2000; Escobar et al., 1999; Feng & Ma, 2001; Kobayashi, 1989; Li et al., 2001; Phat, 2001, 2002; Stilwell & Bishop, 2000; Sasu & Sasu, 2004; Sasu, 2006; Tsinias, 1991a, and the references therein). In the stability literature, we can find two major… (More)