Article
Mathematics, Applied
Arpad Baricz, Nitin Bisht, Sanjeev Singh, V. Antony Vijesh
Summary: This paper presents a detailed analysis of a new special function called the generalized Marcum function of the second kind, comparing it with the first kind and exploring the possibility of extending properties from the first kind to the second kind.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Arpad Baricz, Nitin Bisht, Sanjeev Singh, V. Antony Vijesh
Summary: In this paper, the generalized Marcum function of the second kind is considered as an analogous function of the generalized Marcum Q-function, with properties of log-convexity and log-concavity for its unit complement discussed and previous results improved. The transformed functions and important inequalities of the generalized Marcum function of the second kind are detailed, along with a discussion on the Turan type inequality for the generalized Marcum Q-function. Bounds for the generalized Marcum function of the second kind and its symmetric difference are also provided.
RESULTS IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Robert E. Gaunt
Summary: Simple upper and lower bounds are obtained for the integral of interest, with most bounds being tight as x approaches infinity. An inequality is applied to bound some expressions involving the integral, which will advance the technical aspects of variance-gamma approximation in Stein's method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Review
Mathematics, Applied
Robert E. Gaunt
Summary: In this study, simple upper and lower bounds were established for a specific integral involving modified Struve functions, providing sharper bounds or wider ranges of validity. Monotonicity results and inequalities for products of modified Struve functions and modified Bessel functions, as well as a new bound for a specific ratio of these functions, were also obtained in the process of deriving these bounds.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Multidisciplinary Sciences
Robert Reynolds, Allan Stauffer
Summary: Closed expressions for a number of septuple integrals involving the product of three Bessel functions of the first kind are derived using the Hurwitz-Lerch zeta function. These expressions are applicable when the orders of the Bessel functions are large. However, evaluating the integrals for complex values of the parameters is not easy. All the results presented in this work are new.
Article
Mathematics
Arpad Baricz, Nitin Bisht, Sanjeev Singh, V. Antony Vijesh
Summary: This paper focuses on finding new tight bounds for the generalized Marcum function of the second kind and compares them with existing bounds. The monotonicity properties of various functions containing modified Bessel functions of the second kind are used as the main tools to derive these bounds. It is demonstrated that the obtained bounds are the best possible ones in some sense.
Article
Mathematics
Mohammed Fadel, Nusrat Raza, Wei-Shih Du
Summary: In this paper, the q-Bessel functions of the first kind are characterized and their properties are explored using identities of q-calculus. The results obtained help in obtaining new expression results related to q-special functions and new summation and integral representations for q-Bessel functions are established. The effectiveness of the proposed strategy is demonstrated through several examples.
Article
Mathematics
Nuttapong Arunrat, Keaitsuda Maneeruk Nakprasit, Kamsing Nonlaopon, Praveen Agarwal, Sotiris K. Ntouyas
Summary: In this paper, new Chebyshev-type integral inequalities for synchronous functions are established using (p,q)-calculus, and the results are generalized and compared with quantum Chebyshev-type inequalities and classical results on Chebyshev-type inequalities for synchronous functions.
Article
Mathematics
Reem Alzahrani, Saiful R. Mondal
Summary: This paper aims to construct inequalities of the Redheffer type for functions defined by infinite product involving zeroes. The proofs rely on classical results regarding the monotonicity of the ratio of differentiable functions. Special cases lead to examples involving special functions such as Bessel, Struve, and Hurwitz functions, as well as other trigonometric functions.
Article
Mathematics, Applied
Cen Li, Zhi-Ming Liu, Shen-Zhou Zheng
Summary: This paper proves a pair of mathematical inequalities hold under certain conditions, and these results improve some known results.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2022)
Article
Mathematics, Applied
Necmettin Alp
Summary: This study obtained two types of Wirtinger q-inequalities in quantum calculus and proved a more general Wirtinger q-integral inequality. These results lead to classical results as q approaches 1(-).
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Multidisciplinary Sciences
Silvestru Sever Dragomir
Summary: This paper presents several bounds for the modulus of the complex Cebysev functional, along with applications to the trapezoid and mid-point inequalities, which are symmetric inequalities.
Article
Computer Science, Interdisciplinary Applications
Bin Li, Hongchao Kang, Songliang Chen, Shanjing Ren
Summary: This paper addresses the approximation problem of Volterra integral equations of the first kind with highly oscillatory Bessel kernel. A lemma on coefficient relations of different interpolation polynomials is proposed, followed by the existence and uniqueness theorem for the solution of the integral equation. Explicit formulas for the solution are derived based on Laplace transform and inverse Laplace transform. Additionally, simplified approximations are obtained through the asymptotic analysis of the solution for large parameter values. Two numerical methods, efficient quadrature rule and Clenshaw-Curtis-type method, are introduced to efficiently compute the highly oscillatory integrals in the solution of the integral equation.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics
Arshad Hussain, Gauhar Rahman, Jihad Younis, Muhammad Samraiz, Muhammad Iqbal
Summary: This paper aims to estimate new fractional integral inequalities for the extended Chebyshev functional using the fractional integral operator defined in terms of extended generalized Bessel function. A set of inequalities for the fractional integral operator with one and two parameters is proved, and some special cases of the obtained result are discussed.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
Ahmet Ocak Akdemir, Saad Ihsan Butt, Muhammad Nadeem, Maria Alessandra Ragusa
Summary: This study obtained new and general variants on Chebyshev's inequality by using integrable functions and generalized fractional integral operators, generalizing many existing results and iterating the Chebyshev inequality in special cases.
