Analysis of a certain Pseudo $q$-calculus and its applications in integral inequalities
نویسندگان
1 Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran.
2 Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran.
3 Institute of Science and Technology, Federal University of São Paulo, Shariati Ave., São José dos Campos–SP, Brazil.
doi
10.30504/jims.2024.455086.1177چکیده
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.
