Results 21 to 30 of about 86 (65)

Generalizations of the Jensen-Steffensen and related inequalities

Open Mathematics, 2009
Abstract We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.
Pečarić, Josip, Matić, Marko, Klaričić Bakula, Milica   +2 more
openaire   +6 more sources

On the bounds for the normalized Jensen functional and Jensen-Steffensen inequality [PDF]

Mathematical Inequalities & Applications, 2009
We consider the inequalities for normalized Jensen functional, recently introduced by S.S. Dragomir. We give an alternative proof of such inequalities and prove another similar result for the case when f is a convex function on an interval in the real line, while p and q satisfy the conditions for Jensen-Steffensen inequality.
Pečarić, Josip, Matić, Marko, Barić, Josipa   +2 more
openaire   +3 more sources

Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations

Advances in Fuzzy Systems, Volume 2019, Issue 1, 2019., 2019
The classical Hölder inequality shows an interesting upper bound for Lebesgue integral of the product of two functions. This paper proposes Hölder type inequalities and reverse Hölder type inequalities for Sugeno integrals under usual multiplication operations for nonincreasing concave or convex functions.
Dug Hun Hong, Jae Duck Kim, Michal Baczynski   +2 more
wiley   +1 more source

Integral Inequalities Involving Strongly Convex Functions

Journal of Function Spaces, Volume 2018, Issue 1, 2018., 2018
We study the notions of strongly convex function as well as F‐strongly convex function. We present here some new integral inequalities of Jensen’s type for these classes of functions. A refinement of companion inequality to Jensen’s inequality established by Matić and Pečarić is shown to be recaptured as a particular instance.
Ying-Qing Song, Muhammad Adil Khan, Syed Zaheer Ullah, Yu-Ming Chu, Alberto Fiorenza   +4 more
wiley   +1 more source

Generalized Jensen‐Mercer Inequality for Functions with Nondecreasing Increments

Abstract and Applied Analysis, Volume 2016, Issue 1, 2016., 2016
In the year 2003, McD Mercer established an interesting variation of Jensen’s inequality and later in 2009 Mercer’s result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda’s result for convex functions.
Asif R. Khan, Sumayyah Saadi, Wing-Sum Cheung   +2 more
wiley   +1 more source

Generalized Steffensen Type Inequalities Involving Convex Functions

Journal of Function Spaces, Volume 2014, Issue 1, 2014., 2014
In this paper generalized Steffensen type inequalities related to the class of functions that are “convex at point c” are derived and as a consequence inequalities involving the class of convex functions are obtained. Moreover, linear functionals from the difference of the right‐ and left‐hand side of the obtained generalized inequalities are ...
Josip Pečarić, Ksenija Smoljak Kalamir, Hugo Leiva   +2 more
wiley   +1 more source

Improvements of Jensen‐Type Inequalities for Diamond‐α Integrals

International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014
We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left‐hand side and the right‐hand ...
Rabia Bibi, Josip Pečarić, Mirna Rodić Lipanović, Jan L. Cieśliński   +3 more
wiley   +1 more source

On exponential convexity, Jensen-Steffensen-Boas Inequality, and Cauchy's means for superquadratic functions [PDF]

Journal of Mathematical Inequalities, 2011
In this paper we define new means of Cauchy's type using some recently obtained results that refine the Jensen-Steffensen-Boas inequality for convex and superquadratic functions. Applying so called exp-convex method we interpret results in the form of exponentially convex or (as a special case) logarithmically convex functions.
Abramovich, Shoshana, Farid, Ghulam, Ivelić, Slavica, Pečarić, Josip   +3 more
openaire   +3 more sources

Fractional Integral Inequalities for Generalized Interval‐Valued Functions With Applications in Stock Price Prediction via LSTM

Journal of Mathematics, Volume 2026, Issue 1, 2026.
We explore the features of fractional integral inequalities for some new classes of interval‐valued convex functions (CF s) to establish their generalization compared to the previously known real‐valued CF s. Motivated by the foundational role of mathematical inequalities in analysis and optimization, we delve into the formulation and proof of integral
Ahsan Fareed Shah, Patricia J. Y. Wong, Nasir Rehman, Salah Mahmoud Boulaaras, Muhammad Shoaib Saleem, B. B Upadhyay   +5 more
wiley   +1 more source

Reverses of the Jensen‐Type Inequalities for Signed Measures

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
In this paper we derive refinements of the Jensen type inequalities in the case of real Stieltjes measure dλ, not necessarily positive, which are generalizations of Jensen′s inequality and its reverses for positive measures. Furthermore, we investigate the exponential and logarithmic convexity of the difference between the left‐hand and the right‐hand ...
Rozarija Jakšić, Josip Pečarić, Mirna Rodić Lipanović, Shawn X. Wang   +3 more
wiley   +1 more source