271 citations · 1.8k across the 55 of their papers we have counts for
11 papers · 1 filter
A Study of Diamond-alpha dynamic equations on regular time scales
Dorota Mozyrska, Delfim F. M. Torres
We introduce the diamond-alpha exponential function on time scales. As particular cases, one gets both delta and nabla exponential functions. A method of solution of a homogenous l…
A mu-differentiable Lagrange multiplier rule
Ricardo Almeida, Delfim F. M. Torres
We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.
Relaxed optimality conditions for mu-differentiable functions
Ricardo Almeida, Delfim F. M. Torres
We prove some fundamental properties of mu-differentiable functions. A new notion of local minimizer and maximizer is introduced and several extremum conditions are formulated usin…
Some linear and nonlinear integral inequalities on time scales in two independent variables
Rui A. C. Ferreira, Delfim F. M. Torres
We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are il…
Generalizations of Gronwall-Bihari Inequalities on Time Scales
Rui A. C. Ferreira, Delfim F. M. Torres
We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some…
Diamond-alpha Polynomial Series on Time Scales
Dorota Mozyrska, Delfim F. M. Torres
The objective of this paper is twofold: (i) to survey existing results of generalized polynomials on time scales, covering definitions and properties for both delta and nabla deriv…