Abstract
In this paper, we present a variety of existence theorems for maximal type elements in a general setting. We consider multivalued maps with continuous selections and multivalued maps which are admissible with respect to Gorniewicz and our existence theory is based on the author’s old and new coincidence theory. Particularly, for the second section we present presents a collectively coincidence coercive type result for different classes of maps. In the third section we consider considers majorized maps and presents a variety of new maximal element type results. Coincidence theory is motivated from real-world physical models where symmetry and asymmetry play a major role.
Highlights
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Using some collectively fixed and coincidence type results of the author [1,2] and a new general collectively coincidence result in Section 2 of this paper we present some new maximal type element theorems for families of majorized type maps [3,4]
In [2], the author presented collectively coincidence type results between maps in the same classes and the idea there (see [2] (Theorem 2.15)) was to generate continuous single valued selections for appropriate maps and use a single valued map with the Brouwder fixed point theorem to conclude the existence of a coincidence
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In [2], the author presented collectively coincidence type results between maps in the same classes and the idea there (see [2] (Theorem 2.15)) was to generate continuous single valued selections for appropriate maps and use a single valued map with the Brouwder fixed point theorem to conclude the existence of a coincidence.
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