Abstract

We study Aumann-Pettis integrable multifunctions on 2X2^X, where X is a separable Banach space and their integrals. We prove the existence of a weakly compact convex-valued Pettis integrable multifunction F for a closed, convex, decomposable and weakly sequentially compact subset K of P1(μ,X)P_1(\mu, X), the space of all Pettis integrable functions on X such that K coincides with SFPS_F^P, the collection of all Pettis integrable selectors of F. We also study the weak compactness property of SFPS_F^P.

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Nanda Dulal Chakraborty

Dept. of Mathematics, University of Burdwan, Burdwan 713104, West Bengal – India

cms_ndc@yahoo.co.in

Tanusree Choudhury

Dept. of Mathematics, Raja Peary Mohan College, Calcutta University, Hooghly 712258, West Bengal – India

choudhurytanusree@yahoo.co.in

Keywords

  • Aumann-Pettis integrable multifunctions
  • Pettis integrable multifunctions
  • Aumann-Pettis integral
  • Pettis integral
  • weak convergence

Mathematics Subject Classification

46G10, 46E30, 46P10; 28B20, 54C60

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Suggested citation

N. D. Chakraborty, T. Choudhury. “On Some Properties of Pettis Integrable Multifunctions.” Journal of Convex Analysis 19 (2012), No. 3, 671–683. https://doi.org/10.68381/jca19036

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.