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The class -KKM(X,Y,Z) and generalized KKM mapping are introduced, and some generalized KKM theorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results

abstract and applied analysis

Class<i>𝔄</i>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>K</mml:mi><mml:mi>K</mml:mi><mml:mi>M</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi><mml:mo>,</mml:mo><mml:mi>Z</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, General<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>K</mml:mi><mml:mi>K</mml:mi><mml:mi>M</mml:mi></mml:math>Type Theorems…

Class𝔄-KKM(X,Y,Z), GeneralKKMType Theorems…