In this note, natural exponential bounds for coshx are established. The inequalities thus obtaine... more In this note, natural exponential bounds for coshx are established. The inequalities thus obtained are interesting and sharp.
We present new generalized lower and upper bounds for the natural exponential function. These bou... more We present new generalized lower and upper bounds for the natural exponential function. These bounds are algebraic in nature and each involve a parameter a. Each bound is optimal as a → 0.
In this work, the authors present new lower and upper bounds for cos x and cosh x, thus improving... more In this work, the authors present new lower and upper bounds for cos x and cosh x, thus improving some generalized inequalities of Kober and Lazarevic type.
In this paper, we determine new and sharp inequalities involving trigonometric functions. More sp... more In this paper, we determine new and sharp inequalities involving trigonometric functions. More specifically, a new general result on the lower bound for log(1−uv), u, v ∈ (0, 1) is proved, allowing to determine sharp lower and upper bounds for the so-called sinc function, i.e., sin(x)/x, lower bounds for cos(x) and upper bounds for (cos(x/3)) 3. The obtained bounds improve some well-established results. The findings are supported by graphical analyses
This paper presents a new method for approximating the classical arcsine function. The proposed a... more This paper presents a new method for approximating the classical arcsine function. The proposed approximating methodology is simpler in its approach than other classical approaches and undeniably innovative. It is based on matrix representation besides the basic interpolation to approximate the inverse trigonometric function. It provides an efficient model which allows for reliable and precise calculations. The results are as per our knowledge unseen results in the previous literature.
We present new generalized lower and upper bounds for the natural exponential function. These bou... more We present new generalized lower and upper bounds for the natural exponential function. These bounds are algebraic in nature and each involve a parameter a. Each bound is optimal as a → 0.
Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbol... more Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions.
Using convexity and double-sided Taylor's approximations of functions, we establish new gener... more Using convexity and double-sided Taylor's approximations of functions, we establish new general results in this field which can be used to refine and/or sharp some analytic inequalities in the existing literature.
In this note, natural exponential bounds for coshx are established. The inequalities thus obtaine... more In this note, natural exponential bounds for coshx are established. The inequalities thus obtained are interesting and sharp.
We present new generalized lower and upper bounds for the natural exponential function. These bou... more We present new generalized lower and upper bounds for the natural exponential function. These bounds are algebraic in nature and each involve a parameter a. Each bound is optimal as a → 0.
In this work, the authors present new lower and upper bounds for cos x and cosh x, thus improving... more In this work, the authors present new lower and upper bounds for cos x and cosh x, thus improving some generalized inequalities of Kober and Lazarevic type.
In this paper, we determine new and sharp inequalities involving trigonometric functions. More sp... more In this paper, we determine new and sharp inequalities involving trigonometric functions. More specifically, a new general result on the lower bound for log(1−uv), u, v ∈ (0, 1) is proved, allowing to determine sharp lower and upper bounds for the so-called sinc function, i.e., sin(x)/x, lower bounds for cos(x) and upper bounds for (cos(x/3)) 3. The obtained bounds improve some well-established results. The findings are supported by graphical analyses
This paper presents a new method for approximating the classical arcsine function. The proposed a... more This paper presents a new method for approximating the classical arcsine function. The proposed approximating methodology is simpler in its approach than other classical approaches and undeniably innovative. It is based on matrix representation besides the basic interpolation to approximate the inverse trigonometric function. It provides an efficient model which allows for reliable and precise calculations. The results are as per our knowledge unseen results in the previous literature.
We present new generalized lower and upper bounds for the natural exponential function. These bou... more We present new generalized lower and upper bounds for the natural exponential function. These bounds are algebraic in nature and each involve a parameter a. Each bound is optimal as a → 0.
Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbol... more Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended. Hyperbolic versions are also established, along with extensions.
Using convexity and double-sided Taylor's approximations of functions, we establish new gener... more Using convexity and double-sided Taylor's approximations of functions, we establish new general results in this field which can be used to refine and/or sharp some analytic inequalities in the existing literature.
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Papers by Yogesh J Bagul