This research work considers the following inequalities: <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,&l...This research work considers the following inequalities: <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) and <em>C</em>[<i>λ</i><em>a</em> + (1-<i>λ</i>)<em>b</em>, <i>λ</i><em>b</em> + (1-<i>λ</i>)<em>a</em>] ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <em>C</em>[<i>μ</i><em>a</em> + (1-<i>μ</i>)<em>b</em>, <i>μ</i><em>b</em> + (1-<i>μ</i>)<em>a</em>] with <img src="Edit_ce892b1d-c056-44ea-a929-31dbcd1b0e91.bmp" alt="" /> . The researchers attempt to find an answer as to what are the best possible parameters <i>λ</i>, <i>μ</i> that (1.1) and (1.2) can be hold? The main tool is the optimization of some suitable functions that we seek to find out. By searching the best possible parameters such that (1.1) and (1.2) can be held. Firstly, we insert <em>f</em>(<i>t</i>) = <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_efa43881-9a60-44f8-a86f-d4a1057f4378.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become f (<i>t</i>) ≤ 0. Secondly, we insert g(<i>t</i>) = <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_750dddbb-1d71-45d3-be29-6da5c88ba85d.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become <em>g</em>(<i>t</i>) ≥ 0.展开更多
In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters <i><i>α</i></i>, <i><i&...In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters <i><i>α</i></i>, <i><i>β</i></i> that (1.1) can be held? The main tool is the optimization of some suitable functions that we seek to find out. Without loss of generality, we have assumed that <i>a</i> > <i>b</i> and let <img src="Edit_26c0f99b-93dd-48ff-acdb-f1c8047744f1.bmp" alt="" /> for 1) and <i>a</i> < <i>b</i>, <img src="Edit_15c32a7a-e9ae-41d3-8f49-c6b9c01c7ece.bmp" alt="" />(<i>t</i> small) for 2) to determine the condition for <i><i>α</i></i> and <i><i>β</i></i> to become <i>f</i>(<i>t</i>) ≤ 0 and <i>g</i>(<i>t</i>) ≥ 0.展开更多
文摘This research work considers the following inequalities: <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) and <em>C</em>[<i>λ</i><em>a</em> + (1-<i>λ</i>)<em>b</em>, <i>λ</i><em>b</em> + (1-<i>λ</i>)<em>a</em>] ≤ <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) ≤ <em>C</em>[<i>μ</i><em>a</em> + (1-<i>μ</i>)<em>b</em>, <i>μ</i><em>b</em> + (1-<i>μ</i>)<em>a</em>] with <img src="Edit_ce892b1d-c056-44ea-a929-31dbcd1b0e91.bmp" alt="" /> . The researchers attempt to find an answer as to what are the best possible parameters <i>λ</i>, <i>μ</i> that (1.1) and (1.2) can be hold? The main tool is the optimization of some suitable functions that we seek to find out. By searching the best possible parameters such that (1.1) and (1.2) can be held. Firstly, we insert <em>f</em>(<i>t</i>) = <i>λ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>λ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_efa43881-9a60-44f8-a86f-d4a1057f4378.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become f (<i>t</i>) ≤ 0. Secondly, we insert g(<i>t</i>) = <i>μ</i><em>A</em>(<i>a</i>,<i>b</i>) + (1-<i>μ</i>)<em>C</em>(<i>a</i>,<i>b</i>) - <span style="text-decoration:overline;">C</span>(<i>a</i>,<i>b</i>) without the loss of generality. We assume that <i>a</i>><i>b</i> and let <img src="Edit_750dddbb-1d71-45d3-be29-6da5c88ba85d.bmp" alt="" /> to determine the condition for <i>λ</i> and <i>μ</i> to become <em>g</em>(<i>t</i>) ≥ 0.
文摘In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters <i><i>α</i></i>, <i><i>β</i></i> that (1.1) can be held? The main tool is the optimization of some suitable functions that we seek to find out. Without loss of generality, we have assumed that <i>a</i> > <i>b</i> and let <img src="Edit_26c0f99b-93dd-48ff-acdb-f1c8047744f1.bmp" alt="" /> for 1) and <i>a</i> < <i>b</i>, <img src="Edit_15c32a7a-e9ae-41d3-8f49-c6b9c01c7ece.bmp" alt="" />(<i>t</i> small) for 2) to determine the condition for <i><i>α</i></i> and <i><i>β</i></i> to become <i>f</i>(<i>t</i>) ≤ 0 and <i>g</i>(<i>t</i>) ≥ 0.
