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Title: Orthogonality preserving infinite dimensional quadratic stochastic operators

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey)
  2. Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)
Publication Date:
OSTI Identifier:
22488892
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1676; Journal Issue: 1; Conference: International conference on advancements in mathematical sciences, Antalya (Turkey), 5-7 Nov 2015; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STOCHASTIC PROCESSES; VOLTERRA INTEGRAL EQUATIONS