Abstract
In this paper, the concept of normalized duality mapping has introduced in real convex modular spaces. Then, some of its properties have shown which allow dealing with results related to the concept of uniformly smooth convex real modular spaces. For multivalued mappings defined on these spaces, the convergence of a two-step type iterative sequence to a fixed point is proved
Highlights
Nakano in 1950 (1) introduced the concept of a modular on a linear space and refined by Musielak and Orlicz in 1959 (2): Definition 1 Let M be real linear space
This paper is devoted to presenting several cases of the real modular spaces related to convexity and smooth convexity to be used in the study of the convergence for two types of iterative sequences
The concepts of -normalized duality and uniformly smooth convex mapping in the real convex modular spaces are presented with some interesting properties
Summary
Nakano in 1950 (1) introduced the concept of a modular on a linear space and refined by Musielak and Orlicz in 1959 (2): Definition 1 Let M be real linear space. A function :M is called modular if (i) if and only if. – )} is Hausdorff the following lemma is obtained Lemma 1 Let M be a modular space and and . Definition 7 (8) M is called uniformly convex if for any > 0, there exists a ( ) > 0, if. Is complete convex real modular, is the dual space of. Corollary 1: Let be a subspace of real modular space and a bounded linear functional on. There exists a bounded linear functional F defined on that is an extension of
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