All Stories

  1. Huygens type inequalities for sinhc and tanhc functions
  2. Several new inequalities of tanc function with applications to Seiffert mean
  3. On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function
  4. Several sharp inequalities involving (hyperbolic) tangent, tanc, cosine, and their reciprocals
  5. Several identities and relations related to q-analogues of Pochhammer k-symbol with applications to Fuss–Catalan–Qi numbers
  6. Monotonicity, convexity, and Maclaurin series expansion of Qi's normalized remainder of Maclaurin series expansion with relation to cosine
  7. Determinantal Expressions, Identities, Concavity, Maclaurin Power Series Expansions for van der Pol Numbers, Bernoulli Numbers, and Cotangent
  8. A Sufficient and Necessary Condition for the Power-Exponential Function 1+1xαx to Be a Bernstein Function and Related nth Derivatives
  9. Several integral inequalities of the Hermite-Hadamard type for s-(β, F)-convex functions
  10. Hermite–Hadamard type inequalities for harmonic-arithmetic extended $ (s_1, m_1) $-$ (s_2, m_2) $ coordinated convex functions
  11. Hermite–Hadamard’s Integral Inequalities of (α,s)-GA- and (α,s,m)-GA-Convex Functions
  12. Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean
  13. Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means
  14. Some new integral inequalities of the Simpson type for MT-convex functions
  15. MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function
  16. Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities
  17. Generalizations of Hermite–Hadamard Type Integral Inequalities for Convex Functions
  18. Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios
  19. Direct, Inverse, and Equivalence Theorems for Weighted Szász—Durrmeyer—Bézier Operators in Orlicz Spaces
  20. Coordinated MT- s ...
  21. Some properties of the Hermite polynomials
  22. A ratio of finitely many gamma functions and its properties with applications
  23. Series expansions of powers of arcsine, closed forms for special values of Bell polynomials, and series representations of generalized logsine functions
  24. Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind
  25. Determinantal Formulas and Recurrent Relations for Bi-Periodic Fibonacci and Lucas Polynomials
  26. Inequalities of Hermite-Hadamard type for extended harmonically (s,m)-convex functions
  27. Necessary and sufficient conditions on the Schur convexity of a bivariate mean
  28. Refinements of Young’s Integral Inequality via Fundamental Inequalities and Mean Value Theorems for Derivatives1
  29. Several Explicit and Recurrent Formulas for Determinants of Tridiagonal Matrices via Generalized Continued Fractions
  30. Retraction Note to: A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant
  31. From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
  32. Closed formulas and identities on the Bell polynomials and falling factorials
  33. Some properties and an application of multivariate exponential polynomials
  34. Correction: Monotonicity and inequalities related to complete elliptic integrals of the second kind
  35. Monotonicity and inequalities related to complete elliptic integrals of the second kind
  36. Several explicit and recursive formulas for generalized Motzkin numbers
  37. Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions
  38. On GT-convexity and related integral inequalities
  39. Relations among Bell polynomials, central factorial numbers, and central Bell polynomials
  40. Generalizations and applications of Young’s integral inequality by higher order derivatives
  41. Equivalent theorem of approximation by linear combination of weighted Baskakov–Kantorovich operators in Orlicz spaces
  42. A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant
  43. Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind
  44. Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind
  45. The inverse of a triangular matrix and several identities of the Catalan numbers
  46. On integral inequalities of Hermite-Hadamard type for coordinated r-mean convex functions
  47. Shannon Type Inequalities for Kapur’s Entropy
  48. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius-Euler Numbers
  49. On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function
  50. Integral Representations of the Large and Little Schröder Numbers
  51. Some identities for a sequence of unnamed polynomials connected with the Bell polynomials
  52. A diagonal recurrence relation for the Stirling numbers of the first kind
  53. Lévy-Khintchine representation of Toader-Qi mean
  54. Some identities related to Eulerian polynomials and involving the Stirling numbers
  55. A representation for derangement numbers in terms of a tridiagonal determinant
  56. A closed form for the Stirling polynomials in terms of the Stirling numbers
  57. An explicit formula for derivative polynomials of the tangent function
  58. Some Inequalities of the Hermite-Hadamard Type for Harmonically Quasi-Convex Functions
  59. The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function
  60. Some properties of the divided difference of psi and polygamma functions
  61. Generalizations of the Bell Numbers and Polynomials and Their Properties
  62. Some Identities for a Sequence of Unnamed Polynomials Connected with the Bell Polynomials
  63. Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations
  64. Simplifying Coefficients in Differential Equations Associated with Higher Order Bernoulli Numbers of the Second Kind
  65. Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers
  66. Integral Representations of the Catalan Numbers and Their Applications
  67. Some Identities Relating to Eulerian Polynomials and Involving Stirling Numbers
  68. Simplifying differential equations concerning degenerate Bernoulli and Euler numbers
  69. Some explicit and recursive formulas of the large and little Schröder numbers
  70. Explicit formulas and recurrence relations for higher order Eulerian polynomials
  71. Some properties of central Delannoy numbers
  72. Explicit Formulas for Special Values of the Bell Polynomials of the Second Kind and for the Euler Numbers and Polynomials
  73. Closed forms for derangement numbers in terms of the Hessenberg determinants
  74. Some properties of a sequence arising from geometric probability for pairs of hyperplanes intersecting with a convex body
  75. Notes on a Family of Inhomogeneous Linear Ordinary Differential Equations
  76. Identities of the Chebyshev Polynomials, the Inverse of a Triangular Matrix, and Identities of the Catalan Numbers
  77. Closed Expressions of the Fibonacci Polynomials in Terms of Tridiagonal Determinants
  78. A criterion to justify a holomorphic function
  79. A Closed Form for the Stirling Polynomials in Terms of the Stirling Numbers
  80. Explicit and recursive formulas, integral representations, and properties of the large Schröder numbers
  81. An explicit formula for Bernoulli polynomials in terms of $\boldsymbol r$-Stirling numbers of the second kind
  82. Some properties of the Schröder numbers
  83. Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations
  84. Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
  85. A Determinantal Expression and a Recurrence Relation for the Euler Polynomials
  86. The reciprocal of the weighted geometric mean is a Stieltjes function
  87. A recovery of two determinantal representations for derangement numbers
  88. The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform
  89. Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers
  90. SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
  91. Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function
  92. Some Generalizations of Integral Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions
  93. Complete monotonicity of divided differences of the di- and tri-gamma functions with applications
  94. Logarithmically complete monotonicity of a function related to the Catalan-Qi function
  95. An inequality involving the gamma and digamma functions
  96. REMARKS ON COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE GAMMA FUNCTION
  97. The additivity of polygamma functions
  98. Sharp Inequalities for Polygamma Functions
  99. A class of completely monotonic functions involving the gamma and polygamma functions
  100. Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind
  101. On the degree of the weighted geometric mean as a complete Bernstein function
  102. Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
  103. Sharp inequalities for the psi function and harmonic numbers
  104. Some identities and an explicit formula for Bernoulli and Stirling numbers
  105. Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions
  106. Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives
  107. A Class of Logarithmically Completely Monotonic Functions and Their Applications
  108. Monotonicity results and inequalities for the inverse hyperbolic sine function
  109. Logarithmically completely monotonic functions and applications
  110. A completely monotonic function involving the tri- and tetra-gamma functions
  111. On proofs for monotonicity of a function involving the psi and exponential functions
  112. Complete monotonicity of a function involving the divided difference of digamma functions
  113. Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
  114. Some properties of completely monotonic sequences and related interpolation
  115. Complete monotonicity of two functions involving the tri-and tetra-gamma functions
  116. Monotonicity of functions connected with the gamma function and the volume of the unit ball
  117. Refinements of lower bounds for polygamma functions
  118. A completely monotonic function involving the tri-gamma function and with degree one
  119. Monotonicity and logarithmic convexity relating to the volume of the unit ball
  120. A refinement of a double inequality for the gamma function
  121. Sharpening and generalizations of Shafer's inequality for the arc sine function
  122. Complete monotonicity of a function involving the ratio of gamma functions and applications
  123. Logarithmic convexity of Gini means
  124. A simple proof of Oppenheim's double inequality relating to the cosine and sine functions
  125. Sharp bounds for harmonic numbers
  126. An extension of an inequality for ratios of gamma functions
  127. A class of completely monotonic functions involving divided differences of the polygamma functions
  128. An alternative proof of Elezović-Giordano-Pečarić's theorem
  129. The function (bx−ax)/x: Logarithmic convexity and applications to extended mean values
  130. Some bounds for the complete elliptic integrals of the first and second kinds
  131. Some uniqueness results for the non-trivially complete monotonicity of a class of functions involving the polygamma and related functions
  132. Some logarithmically completely monotonic functions related to the gamma function
  133. A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE GAMMA FUNCTION
  134. Some properties of extended remainder of binet’s first formula for logarithm of gamma function
  135. Complete monotonicity of some functions involving polygamma functions
  136. Two new proofs of the complete monotonicity of a function involving the psi function
  137. Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic
  138. Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
  139. Properties and applications of a function involving exponential functions
  140. A simple proof of logarithmic convexity of extended mean values
  141. Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems
  142. Sharpening and Generalizations of Shafer's Inequality for the Arc Tangent Function
  143. Wendel’s and Gautschi’s inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions
  144. A class of logarithmically completely monotonic functions
  145. Monotonicity and logarithmic concavity of two functions involving exponential function
  146. Darboux’s formula with integral remainder of functions with two independent variables
  147. Alternative proofs for inequalities of some trigonometric functions
  148. A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality
  149. A class ofk-log-convex functions and their applications to some special functions
  150. A function involving gamma function and having logarithmically absolute convexity
  151. Some completely monotonic functions involving the gamma and polygamma functions
  152. Monotonicity of sequences involving convex function and sequence
  153. Monotonicity of sequences involving geometric means of positive sequences with monotonicity and logarithmical convexity
  154. The best bounds in Gautschi-Kershaw inequalities
  155. Some completely monotonic functions involving polygamma functions and an application
  156. Notes on double inequalities of Mathieu′s series
  157. Some notes on a functional equation
  158. A lower bound for ratio of power means
  159. AN INEQUALITY BETWEEN RATIO OF THE EXTENDED LOGARITHMIC MEANS AND RATIO OF THE EXPONENTIAL MEANS
  160. INEQUALITIES AND MONOTONICITY FOR THE RATIO OF GAMMA FUNCTIONS
  161. On new proofs of Wilker's inequalities involving trigonometric functions
  162. Generalizations of Bernoulli numbers and polynomials
  163. Estimates of an integral in terms of the $L^p$-norm of the $(n+1)$st derivative of its integrand
  164. On Steffensen pairs
  165. Generalization of Bernoulli polynomials
  166. An inductive proof for an identity involving (n k) and the partial sums of some series
  167. Inequalities for Generalized Weighted Mean Values of Convex Function