A5098958579- Mathematical Inequalities and Applications
- Fractional Differential Equations Solutions
- Mathematical functions and polynomials
- Functional Equations Stability Results
- Iterative Methods for Nonlinear Equations
- Matrix Theory and Algorithms
- Advanced Mathematical Theories and Applications
- Nonlinear Waves and Solitons
- Numerical methods in inverse problems
- Mathematics and Applications
- Nonlinear Differential Equations Analysis
- Numerical methods for differential equations
Nanjing Normal University
2024-2025
Integral inequalities are very useful in finding the error bounds for numerical integration formulas. In this paper, we prove some multiplicative integral first-time differentiable s-convex functions. These new help different formulas calculus. The use of function extends results convex functions and covers a large class functions, which is main motivation using s-convexity. To inequalities, derive two identities setting Then, with these identities, Simpson Ostrowski types generalized...
This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type to this domain. An equality involving Riemann–Liouville integrals is established, forming foundation deriving novel tailored functions. The proposed encompasses a wide range functional classes, including Lipschitzian functions, bounded and variation, thereby broadening applicability these diverse mathematical settings. research emphasizes...
The advancement of fractional calculus, particularly through the Caputo derivative, has enabled more accurate modeling processes with memory and hereditary effects, driving significant interest in this field. Fractional calculus also extends concept classical derivatives integrals to noninteger (fractional) orders. This generalization allows for flexible complex phenomena that cannot be adequately described using integer-order derivatives. Motivated by its applications various scientific...
ABSTRACT This study introduces a novel class of the Newton–Cotes‐type inequalities derived from parameterized identity within framework multiplicative calculus. These provide an innovative approach to integral approximation, refining existing results for specific parameter choices, including Midpoint, Trapezoidal, Simpson's, Newton's, Maclaurin's, and Weddle's formulas. development is particularly significant in numerical analysis, where precise approximations are critical, such as solving...
In this article, we develop multiplicative fractional versions of Simpson’s and Newton’s formula-type inequalities for differentiable generalized convex functions with the help established identities. The main motivation using lies in their ability to extend results beyond traditional functions, encompassing a broader class providing optimal approximations both lower upper bounds. These are very useful finding error bounds numerical integration formulas calculus. Applying these Quadrature...
This paper presents a rigorous proof of novel multiplicative integral identity and utilize it to establish new Boole's type inequalities for multiplicatively convex functions. These newly established can be helpful in finding the bounds formula within framework calculus. Moreover, provide best optimal approximations polynomials degree six. Finding an error term using first derivative is excellent achievement inequality theory because class first-time differentiable functions more extensive...