Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Analysis of a certain Pseudo $q$-calculus and its applications in integral inequalities

Document Type : Research Article

Authors
1 Department of‎ ‎Mathematics, Babol Noshirvani University of Technology‎, ‎Shariati Ave., Babol‎, ‎Iran.
2 Institute of Science and Technology, Federal University of São Paulo, Shariati Ave., São José dos Campos–SP, Brazil.
Abstract
We define three new operators which‎, ‎in exceptional cases‎, ‎are reduced to\linebreak $q$-integral/derivative $q_a$-integral/derivative and ${}^bq$-integral/derivative operators‎. ‎Fundamental properties emerge among these specific $q$-operators‎, ‎like fractional calculus‎. By utilizing these three newly introduced operators‎, ‎we can prove various inequalities‎, ‎the most notable of which are the Chebyshev and Hermite-Hadamard types‎. ‎Consequently‎, ‎these new operators provide a generalized approach to many problems in classical inequalities using classical fractional calculus‎.
Keywords
Subjects

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