| Summary: | In this paper, we prove the Hermite–Hadamard–Fejér type inequalities for coordinated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msub><mi>h</mi><mn>1</mn></msub><mo>,</mo><msub><mi>h</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula>-convex functions on the rectangle from the plane <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>2</mn></msup></semantics></math></inline-formula>. Some generalizations of the Hermite–Hadamard-type inequalities of two variables are also obtained as a consequence. Some properties of two functionals which are connected with the coordinated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><msub><mi>h</mi><mn>1</mn></msub><mo>,</mo><msub><mi>h</mi><mn>2</mn></msub></mfenced></semantics></math></inline-formula>-convex functions are provided as well. Finally, we give applications of the acquired results to special means of positive real numbers.
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