Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
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Pinar Karagözoglu
and
Hüseyin Budak
Abstract
In this paper, we first establish a novel integral identity involving functions of two variables by using the Riemann–Liouville fractional integrals. By taking the modulus of this newly derived identity, we obtain a new form of Newton-type inequality specifically for differentiable co-ordinated convex functions. Moreover, we give example using graph in order to show that our main results are correct. In addition, we derive several new inequalities by employing Hölder’s inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems. These results not only extend existing inequalities in the literature but also offer new insights into the interplay between fractional calculus and convex analysis.
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(Communicated by Tomasz Natkaniec)
References
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Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
- Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
