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Subject: search.filters.subject.fractional integral inequalities

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    Refinement of Jensen-type inequalities: fractional extensions (global and local)
    (American Institute of Mathematical Sciences (AIMS), 2025)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Jorge A. Paz Moyado
    ;
    José M. Rodríguez-García
    ;
    José M. Sigarreta
    Scopus© Citations 1  2
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    Some new Milne-type inequalities
    (2024)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    ;
    Eva Tourís
      9
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    On a generalization of the Opial inequality
    (2024)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Ana Portilla
    ;
    Jose M. Rodriguez
    ;
    Jose M. Sigarreta
    Inequalities are essential in pure and applied mathematics. In particular, Opial’s inequality and its generalizations have been playing an important role in the study of the existence and uniqueness of initial and boundary value problems. In this work, some new Opial-type inequalities are given and applied to generalized Riemann-Liouville-type integral operators.
    Scopus© Citations 5  3
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    On new Milne-type inequalities and applications
    (2023)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important role in the study of Rosseland’s integral for the stellar absorption. In this paper we obtain new Milne-type inequalities, and we apply them to the generalized Riemann–Liouville-type integral operators, which include most of the known Riemann–Liouville integral operators.
      18  1Scopus© Citations 23
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    Jensen-type inequalities for <i>m</i>-convex functions
    (2022)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Yamilet Quintana
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work, we prove some new Jensen-type inequalities for <jats:italic>m</jats:italic>-convex functions and apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.
    Scopus© Citations 5  2