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In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function is strictly increasing from $( 0,\infty ) $ onto $( 1,1860/343 ) $ . This not only yields some known and new inequalities for the gamma function, but also gives some completely monotonic functions related to the gamma function. [ABSTRACT FROM AUTHOR]

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered. [ABSTRACT FROM AUTHOR]

By means of real analysis and weight functions, we obtain a few equivalent conditions of two kinds of Hardy-type integral inequalities with the non-homogeneous kernel and parameters. The constant factors related to the gamma function are proved to be the best possible. We also consider the operator expressions and some cases of homogeneous kernel. [ABSTRACT FROM AUTHOR]

By applying the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of exponential function with the best possible constant factor expressed by the gamma function is given. The more accurate equivalent forms, the operator expressions with the norm, the reverses, and some particular cases are considered. [ABSTRACT FROM AUTHOR]

Let c be any real number and let In this note, we establish an integral expression of $u_{n}(c)$, which provides a direct proof of Theorem 1 in (Mortici and Jang in Filomat 7:1535-1539, ). [ABSTRACT FROM AUTHOR]

By means of the way of weight coefficients and technique of real analysis, an extension of a Hardy-Hilbert-type inequality with parameters and a best possible constant factor is given. The equivalent forms, the operator expression with the norm, the reverses and some particular cases are also considered. [ABSTRACT FROM AUTHOR]

By means of the way of weight coefficients, technique of real analysis, and Hermite-Hadamard's inequality, a strengthened version of the Mulholland-type inequality with the best possible constant factor and multi-parameters is given. The equivalent forms, the reverses, the operator expressions and a few particular cases are considered. [ABSTRACT FROM AUTHOR]

In this paper, we consider the degenerate poly-Bernoulli polynomials. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials. [ABSTRACT FROM AUTHOR]

By using real analysis and weight functions, we obtain a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of exponent function with intermediate variables. The constant factor related to the gamma function is proved to be the best possible. We also consider some particular cases and the operator expressions. [ABSTRACT FROM AUTHOR]

By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided. The equivalent forms, the reverses, and the related homogeneous forms with particular parameters are considered. Meanwhile, an extended Hilbert’s integral operator in the whole plane is defined, and the operator expressions for the equivalent inequalities are obtained. [ABSTRACT FROM AUTHOR]