#### Hemant Kumar Pathak, Ismat Beg, Invariant approximations in Banach spaces, Vol. 2018 (2018), Article ID 5, pp. 1-13

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DOI: 10.23952/cot.2018.5

Received November 7, 2017; Accepted February 8, 2018; Published February 17, 2018

Abstract. In this paper, we first introduce a new approach to the classical fixed point theorems for $H^{+}$-type nonexpansive multivalued mappings in Banach spaces and obtain a generalization of the classical Nadler’s fixed point theorem. Based on this generalization of Nadler’s fixed point theorem, we study the invariant approximation and proved several new results by replacing multivalued nonexpansive mappings with $H^{+}$-type multivalued nonexpansive mappings. Several examples are constructed to illustrate the main results.