New Estimates of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-Ostrowski-Type Inequalities within a Class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>n</mml:mi></mml:math>-Polynomial Prevexity of Functions
Humaira Kalsoom, Muhammad Idrees, Dumitru Bǎleanu, Yu‐Ming Chu
Abstract
In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>n</mml:mi></mml:math>-polynomial preinvex functions. We use the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>n</mml:mi></mml:math>-polynomial preinvex functions to develop <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-differentiable function. However, the problem has been proven to utilize the obtained identity, we give <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>-analogues of the Ostrowski-type integrals inequalities which are connected with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mi>n</mml:mi></mml:math>-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.