Paper's Title:

A New Adomian Approach to Solving Integral Equations of Fredholm and Volterra Second Kind

Author(s):

Ouedraogo Seny, Nebie Abdoul Wassiha, Youssouf Pare, Blaise Some

Departement de mathematiques,
Universite Joseph Ki-Zerbo,
Burkina Faso.
E-mail: oseny@yahoo.fr, nebwass@yahoo.fr
pareyoussouf@yahoo.fr, some@univ-ouaga.bf

Abstract:

In order to simplify the resolution of Fredholm and Volterra's second type integral equations, we propose a new approach based on the Adomian Decompositional Method (ADM). We test the new approach on several examples with success.

Paper's Title:

Generalizations of Hermite-Hadamard's Inequalities for Log-Convex Functions

Author(s):

Ai-Jun Li

School of Mathematics and Informatics, Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com

Abstract:

In this article, Hermite-Hadamard's inequalities are extended in terms of the weighted power mean and log-convex function. Several refinements, generalizations and related inequalities are obtained.

Paper's Title:

Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions

Author(s):

P. Kórus, Z. Retkes

Institute of Applied Pedagogy,
Juhász Gyula Faculty of Education,
University of Szeged,
Hattyas utca 10, H-6725 Szeged,
Hungary.
E-mail: korus.peter@szte.hu

65 Manor Road, Desford, LE9 9JQ,
United Kingdom.
E-mail: tigris35711@gmail.com

Abstract:

The well-known Jensen inequality and Hermite--Hadamard inequality were extended using iterated integrals by Z. Retkes in 2008 and then by P. Kórus in 2019. In this paper, we consider analytical convex (concave) functions in order to obtain new refinements of Jensen's inequality. We apply the main result to the classical HM--GM--AM, AM--RMS, triangle inequalities and present an application to the geometric series. We also give Mercer type variants of Jensen's inequality.

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