In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logari...In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.展开更多
In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an ...In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an algorithm is suggested for its solution, the computer application of algorithm has been demonstrated by solving some numerical examples. We have used some other techniques, such as (sen, arithmetic mean, median) to solve the same problems, the results in Table 3 indicate that the new technique in general is promising.展开更多
文摘In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.
文摘In this paper, we have suggested a new technique to transform multi-objective linear programming problem (MOLPP) to the single objective linear programming problem by using Harmonic mean for values of function and an algorithm is suggested for its solution, the computer application of algorithm has been demonstrated by solving some numerical examples. We have used some other techniques, such as (sen, arithmetic mean, median) to solve the same problems, the results in Table 3 indicate that the new technique in general is promising.
