In this work, a basic theorem is established and it is found to be a source of inequalities for circular functions. such as Cusa's, Huygens', Wilker's, the Sandor-Bencze, Carlson's, the Shafer-Fink ine...
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In this work, a basic theorem is established and it is found to be a source of inequalities for circular functions. such as Cusa's, Huygens', Wilker's, the Sandor-Bencze, Carlson's, the Shafer-Fink inequality, and the one in the problem of Oppenheim. Furthermore, these inequalities described above will be extended by this basic theorem. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper, we obtain some new sharp bounds for the exponential functions whose powers involve hyperbolic functions and circular functions, respectively.
In this paper, we obtain some new sharp bounds for the exponential functions whose powers involve hyperbolic functions and circular functions, respectively.
This paper established two new Wilker's inequalities of exponential type for the functions sinx/x2+ tanx/x-2 and x/sinx2+x/tanx-2 bounded by the functions 845 x4 tan(61x/7)61x/742/61 and 245 x4 tan 46 x/14 46 x/14...
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This paper established two new Wilker's inequalities of exponential type for the functions sinx/x2+ tanx/x-2 and x/sinx2+x/tanx-2 bounded by the functions 845 x4 tan(61x/7)61x/742/61 and 245 x4 tan 46 x/14 46 x/14 56/23,respectively.
In this paper, we obtain some improved exponential approximation inequalities for the functions and , and we prove them by using the properties of Bernoulli numbers and new criteria for the monotonicity of quotient of...
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In this paper, we obtain some improved exponential approximation inequalities for the functions and , and we prove them by using the properties of Bernoulli numbers and new criteria for the monotonicity of quotient of two power series.
The Walsh series coefficients for the circular functions are considered. Specifically we determine the sequency content of eJptand present bounds on the corresponding sequency-line spectrum.
The Walsh series coefficients for the circular functions are considered. Specifically we determine the sequency content of eJptand present bounds on the corresponding sequency-line spectrum.
In this paper, six new Redheffer-type inequalities involving circular functions and hyperbolic functions are established. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, six new Redheffer-type inequalities involving circular functions and hyperbolic functions are established. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, an unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities for circular functions is established, and the analogue one of Lazarevic and Cusa-Huygens-type inequalities for hyperbolic functions is pres...
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In this paper, an unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities for circular functions is established, and the analogue one of Lazarevic and Cusa-Huygens-type inequalities for hyperbolic functions is presented. At the same time, the new inequality for circular functions is extended to another interval.
Using classical analytic techniques, the Wilker-Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the San...
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Using classical analytic techniques, the Wilker-Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the Sandor-Bencze inequality. (C) 2011 Published by Elsevier Ltd
In this paper, sharp Mitrinovic-Adamovic type inequalities for circular functions is established, and the analogue one of Lazarevic-type inequalities for hyperbolic functions is proved by a simple method. At the same ...
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In this paper, sharp Mitrinovic-Adamovic type inequalities for circular functions is established, and the analogue one of Lazarevic-type inequalities for hyperbolic functions is proved by a simple method. At the same time, the new double inequality for circular functions is extended to another interval.
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