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Start Over Search Limiters Full Text Topic convex functions Publication Year Range Last 10 years Journal cogent mathematics
11 results

1. Some integral inequalities for m-convex functions via generalized fractional integral operator containing generalized Mittag-Leffler function.

Author

Abbas, G., Farid, G., and Liu, Lishan

Subjects
*HADAMARD matrices, *INTEGRAL inequalities, *MATHEMATICAL inequalities, *CONVEX functions, *FRACTIONAL integrals
Abstract

In this paper, we are interested to prove some Hadamard and Fejér-Hadamard-type integral inequalities for m-convex functions via generalized fractional integral operator containing the generalized Mittag-Leffler function. In connection with we obtain some known results. [ABSTRACT FROM AUTHOR]

Published
2016
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2. Some new inequalities of the Hermite-Hadamard type for extended ((s1, m1)-(s2, m2))-convex functions on co-ordinates.

Author

Xi, Bo-Yan, He, Chun-Ying, Qi, Feng, and Srivastava, Hari M.

Subjects
*CONVEX functions, *ANALYTIC geometry, *MATHEMATICAL inequalities, *HERMITE polynomials, *HADAMARD matrices
Abstract

In the paper, the authors introduce a new concept "extended ((s1, m1)-(s2, m2))-convex function on co-ordinates" and establish some new inequalities of the Hermite-Hadamard type for extended ((s1, m1)-(s2, m2))-convex functions of 2 variables on co-ordinates. [ABSTRACT FROM AUTHOR]

Published
2016
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3. Properties and inequalities for the (h1, h2)- and (h1, h2, m)-GA-convex functions.

Author

Xi, Bo-Yan, Qi, Feng, and Liu, Lishan

Subjects
*CONVEX functions, *REAL variables, *INTEGRAL inequalities, *MATHEMATICAL inequalities, *INTEGRALS
Abstract

In the paper, the authors introduce definitions of the (h1, h2)-GA-convex functions and the (h1, h2, m)-GA-convex functions, discuss some properties of these kinds of functions, establish some integral inequalities for these functions, and apply these inequalities to construct several more inequalities. [ABSTRACT FROM AUTHOR]

Published
2016
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4. Bounds on Hankel determinant for starlike and convex functions with respect to symmetric points.

Author

Mishra, Ambuj K., Prajapat, Jugal K., Maharana, Sudhananda, and Srivastava, Hari M.

Subjects
*MATHEMATICAL bounds, *HANKEL functions, *CONVEX functions, *MATHEMATICS, *REAL variables
Abstract

In the present paper, we investigate upper bounds on the third Hankel determinants for the starlike and convex functions with respect to symmetric points in the open unit disk. [ABSTRACT FROM AUTHOR]

Published
2016
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5. Some new Hermite-Hadamard type inequalities for differentiable co-ordinated convex functions.

Author

Guo, Xu-Yang, Qi, Feng, Xi, Bo-Yan, and Boglaev, Igor

Subjects
*HADAMARD matrices, *MATHEMATICAL inequalities, *MATHEMATICAL variables, *CONVEX functions, *LEBESGUE integral
Abstract

In the paper, the authors establish some new Hermite-Hadamard type inequalities for differentiable co-ordinated convex functions of two variables. [ABSTRACT FROM AUTHOR]

Published
2015
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6. Integral inequalities of Hermite-Hadamard type for logarithmically h-preinvex functions.

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Awan, Muhammad Uzair, and Qi, Feng

Subjects
*INTEGRAL inequalities, *CONVEX functions, *HADAMARD matrices, *CONTINUOUS functions, *VARIATIONAL inequalities (Mathematics)
Abstract

In the paper, the authors introduce the notion "logarithmically h-preinvex functions", reveal that the class of h-preinvex functions include several new and known classes of preinvex functions, and establish several integral inequalities of Hermite-Hadamard type. [ABSTRACT FROM AUTHOR]

Published
2015
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7. Generalization of Jensen-type linear functional on time scales via lidstone polynomial.

Author

Bibi, Rabia, Nosheen, Ammara, Pečarić, Josip, and Srivastava, Hari M.

Subjects
*JENSEN'S inequality, *INTEGRALS, *CONVEX functions, *FUNCTIONALS, *POLYNOMIALS
Abstract

In this paper, we prove Jensen’s inequality for diamond integrals on time scales and generalize this inequality for 2n-convex functions via Lidstone’s polynomials. Bounds for Čhebyšhev functional, Grüss-type inequality and Ostrowaski-type inequality related to Jensen’s type functional are also given in the paper. Moreover, our results are valid if we replace diamond integrals with delta integrals, nabla integrals or -diamond integrals on time scales as well (being special cases). [ABSTRACT FROM AUTHOR]

Published
2017
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8. On Hadamard-type inequalities for differentiable functions via Caputo <italic>k</italic>-fractional derivatives.

Author

Farid, Ghulam, Javed, Anum, Rehman, Atiq ur, Qureshi, Muhammad Imran, and Liu, Lishan

Subjects
*MATHEMATICAL inequalities, *CAPUTO fractional derivatives, *CONVEX functions, *MATHEMATICAL bounds, *MATHEMATICAL functions
Abstract

In this paper, we prove a version of the Hadamard inequality for function f such that is convex via k-fractional Caputo derivatives. Using convexity of , we find the bounds of the difference of fractional differential inequality. Also we have found inequalities for Caputo fractional derivatives. [ABSTRACT FROM AUTHOR]

Published
2017
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9. On Hadamard-type inequalities for differentiable functions via Caputo k-fractional derivatives

Author

Ghulam Farid, Atiq Ur Rehman, Muhammad Imran Qureshi, and Anum Javed

Subjects
Pure mathematics, convex functions, lcsh:Mathematics, 010102 general mathematics, Mathematical analysis, Regular polygon, Mathematics::Classical Analysis and ODEs, 010103 numerical & computational mathematics, Function (mathematics), Type (model theory), Caputo fractional derivatives, lcsh:QA1-939, 01 natural sciences, Convexity, Fractional calculus, General Energy, Hadamard inequality, Hadamard transform, Differentiable function, 0101 mathematics, Convex function, Mathematics
Abstract

In this paper, we prove a version of the Hadamard inequality for function f such that $ f^{(n)} $ is convex via k-fractional Caputo derivatives. Using convexity of $ |f^{(n)}|^q $, $ q \ge 1 $ we find the bounds of the difference of fractional differential inequality. Also we have found inequalities for Caputo fractional derivatives.

Published
2017

10. Integral inequalities of Hermite–Hadamard type for logarithmically h-preinvex functions

Author

Feng Qi, Muhammad Uzair Awan, Muhammad Aslam Noor, and Khalida Inayat Noor

Subjects
Discrete mathematics, Class (set theory), convex functions, Hermite polynomials, Hermite–Hadamard type inequality, Logarithmically concave function, lcsh:Mathematics, logarithmically h-preinvex function, Type (model theory), lcsh:QA1-939, General Energy, Hadamard transform, Convex function, Mathematics
Abstract

In the paper, the authors introduce the notion “logarithmically h-preinvex functions”, reveal that the class of h-preinvex functions include several new and known classes of preinvex functions, and establish several integral inequalities of Hermite–Hadamard type.

Published
2015

11. Some integral inequalities for m-convex functions via generalized fractional integral operator containing generalized Mittag-Leffler function

Author

Ghulam Farid and G. Abbas

Subjects
convex functions, Pure mathematics, Mathematics::Classical Analysis and ODEs, 010103 numerical & computational mathematics, 01 natural sciences, Fourier integral operator, symbols.namesake, Operator (computer programming), Hadamard inequality, Mathematics::Probability, Mittag-Leffler function, Improper integral, 0101 mathematics, Mathematics, Mathematics::Complex Variables, lcsh:Mathematics, 010102 general mathematics, Mathematical analysis, Riemann integral, lcsh:QA1-939, Fractional calculus, General Energy, symbols, fractional integral operators, Mittag–Leffler function, Daniell integral, Convex function
Abstract

In this paper, we are interested to prove some Hadamard and Fejér–Hadamard-type integral inequalities for m-convex functions via generalized fractional integral operator containing the generalized Mittag-Leffler function. In connection with we obtain some known results.

Published
2016