Editorial: Overview and Some New Directions.

The notion of competing HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math> ht -Laplacians with weights is considered for the first time. They are driven by a degenerated HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math> ht -Laplacian with weights and a competing HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math> ht -Laplacian with weights, respectively. Finally, the authors indicate how the result can be extended to HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math> ht -equations ( HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mo>/=</mo><mn>2</mn></mrow></semantics></math> ht ). This research aims to present a linear operator HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi mathvariant="script">L</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow><mrow><mi> </mi><mo>,</mo><mi> </mi><mo>,</mo><mi> </mi></mrow></msubsup><mi>f</mi></mrow></semantics></math> ht by utilizing the I q i -Mittag-Leffler function and to introduce the subclass of harmonic HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></semantics></math> ht -convex functions HT <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">HT</mi><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msub><mrow><mo>(</mo><mi> </mi><mo>,</mo><mi mathvariant="script">W</mi><mo>,</mo><mi mathvariant="script">V</mi><mo>)</mo></mrow></mrow></semantics></math> ht related to the Janowski function. [Extracted from the article]