جستجوی مقالات مرتبط با کلیدواژه « integral inequality » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «integral inequality» در نشریات گروه «علوم پایه»-
In this paper, we have proved Diaz-Metcalf inequality for fuzzy integrals. More precisely:\\If $f, g: [0, 1]\to\mathbb{R}$ are continuous and strictly increasing functions, then the fuzzy integral inequality$$ - \hspace{-1em} \int_0^1 f^s d\mu\cdot - \hspace{-1em} \int_0^1 g^sd\mu\le - \hspace{-1em} \int_0^1\left(f\cdot g\right)^sd\mu,$$holds, where $s>1$ and $\mu$ is the Lebesgue measure on $\mathbb{R}$. In addition, we have shown this inequality for pseudo-integrals.
Keywords: Diaz-Metcalf type inequality, Fuzzy integral, integral inequality, pseudo integral} -
In this paper, we prove a new integral identity, and then we establish some new Ostrowski's inequalities for fonctions whose first derivatives are harmonically quasi-convex via Riemann-Liouville fractional integrals.Keywords: integral inequality, Ostrowski inequality, harmonically quasi-convex functions}
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International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023, PP 2031 -2039In this paper, we establish two new refinements for integral forms of Jensen’s and Holder’s inequalities. Several applications are given on special means.Keywords: Jensen’s inequality, Holder’s inequality, Integral inequality}
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In this paper, we introduce the class of strongly $m$--$MT$-convex functions based on the identity given in [P. Cerone et al., 1999]. We establish new inequalities of the Ostrowski-type for functions whose $n^{th}$ derivatives are strongly $m$--$MT$-convex functions.Keywords: Integral inequality, MT-convex functions, Strongly MT-convexity, Strongly m-MT-convexity}
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In this paper, we investigate Godunova type inequality for Sugeno integrals in two cases. At the first case, we suppose that the inner integral is the Riemann integral and the remaining two integrals are of Sugeno type. At the second case, all the integrals are assumed Sugeno integrals. We present several examples to illustrate validity of our results.
Keywords: Sugeno integral, Godunova's inequality, Integral inequality} -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022, PP 371 -378
Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z)=nP(z)+(α−z)P′(z) denote the polar derivative of P(z) with respect to a complex number α. In this paper, we prove some Lr inequalities for the polar derivative of a polynomial have all zeros in |z|≤1. Our theorem generalizes a result of Dewan and Mir [K. K. Dewan, A. Mir, {\it Inequalities for the polar derivative of a polynomial}, J. Interd. Math. 10 (2007), no. 4, 525--531] and includes as special cases several interesting many known results.
Keywords: Polar derivative, Inequality of polynomials, Integral inequality, Zeros} -
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 1, Winter-Spring 2022, PP 523 -537
In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions and on nonlinear functions involved in integrodifferential equations. Further, we extend the integral inequality for piece-wise continuous functions to mixed case and apply it to investigate the dependence of solution on initial data through $epsilon$-approximate solutions. It is seen that the uniqueness and dependency results got by means of integral inequity requires less restrictions on the functions involved in the equations than that required through Picard operators theory.
Keywords: Volterra-Fredholm equation, Integral inequality, Impulse condition, ϵ-approximatesolution, Dependence of solutions} -
International Journal Of Nonlinear Analysis And Applications, Volume:12 Issue: 2, Summer-Autumn 2021, PP 363 -374
In this paper we prove several sharp inequalities that are new versions and extensions of Jensen and $H-H$ inequalities. Then we apply them on means.
Keywords: Jensen’s inequality, Hermite-Hadamard inequality, Integral inequality, Identric mean, Logarithmic mean} -
International Journal of Mathematical Modelling & Computations, Volume:10 Issue: 3, Summer 2020, PP 203 -225In this study, we first introduce the co-ordinated hyperbolic ρ-convex functions. Then we establish some Hermite-Hadamard type inequalities for co-ordinated hyperbolic ρ-convex functions. The inequalities obtained in this study provide generalizations of some results given in earlier works.Keywords: Convex function, hyperbolic ρ-convex functions, Hermite-Hadamard inequality, integral inequality}
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In this note, we give some estimates of the generalized quadratureformula of Gauss-Jacobi type for phi-preinvex functions.
Keywords: Integral inequality, $varphi $-preinvex function, H ̈older inequality, powermean inequality} -
In this article, we study some existence, uniqueness and Ulam type stability results for a class of boundary value problem for nonlinear fractional integro--differential equations with positive constant coefficient involving the Caputo fractional derivative. The main tools used in our analysis is based on Banach contraction principle, Schaefer's fixed point theorem and Pachpatte's integral inequality. Finally, results are illustrated with suitable example.Keywords: Boundary value conditions, Caputo's fractional derivative, Fixed point, integral inequality, Stability}
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International Journal Of Nonlinear Analysis And Applications, Volume:11 Issue: 2, winter spring 2020, PP 379 -390In this paper we establish an extension of Hermite-Hadamard inequality and as a result we obtain the Hermite-Hadamard inequality for fractional integral and logarithmic integral. Also we get a new refinement of it. Some examples are given.Keywords: Hermite-Hadamard inequality, Riemann-Liouille, Fractional integrals, Integral inequality}
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International Journal Of Nonlinear Analysis And Applications, Volume:9 Issue: 2, Summer-Autumn 2018, PP 145 -159In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of obtained results and few illustrative examples.Keywords: Volterra-Fredholm integrodifferential equations, Ulam-Hyers stability, Ulam-Hyers--Rassias stability, Integral inequality, Picard operator}
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International Journal Of Nonlinear Analysis And Applications, Volume:9 Issue: 1, Summer - Autumn 2018, PP 211 -221In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.Keywords: integral inequality, log-convex function, H?lder inequality, power mean inequality}
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International Journal Of Nonlinear Analysis And Applications, Volume:8 Issue: 1, Summer - Autumn 2017, PP 331 -336In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi
aη(b,a) Z a (x−a)p (a η (b,a)−x)q f (x)dx
in the cases where f and |f|λ for λ > 1, are s-preinvex functions in the second sense.Keywords: integral inequality, s, preinvex function, Ho¨lder inequality, power mean inequality} -
In this paper, we prove some integral inequalities, where the right hand side of some inequalities involve the Laplace transformation.
Keywords: Integral inequality, Hardy’s inequality, Hardy-Hilbert’s inequality, Laplace transformation} -
In this paper, we present recent results in integral inequality theory. Our results are based on the fractional integration in the sense of Riemann-Liouville.Keywords: Integral inequality, Riemann, Liouville integral operator}
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In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.Keywords: Hilbert's inequality, Hilbert, type inequality, integral inequality}
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