Abstract
The aim of this paper is to study the convergence of an iteration scheme for multi-valued mappings which defined on a subset of a complete convex real modular. There are two main results, in the first result, we show that the convergence with respect to a multi-valued contraction mapping to a fixed point. And, in the second result, we deal with two different schemes for two multivalued mappings (one of them is a contraction and other has a fixed point) and then we show that the limit point of these two schemes is the same. Moreover, this limit will be the common fixed point the two mappings.
Highlights
Introduction and PreliminariesThe notion of modular spaces was introduced by Nakano [1] in 1950 as a generalization of metric spaces and redefined and modified by Musielak and Ortiz [2] in 1959
Further and the most complete development of these theories are due to Orlicz, Mazur, Musielak, Luxemburg,Turpin [7] and their collaborators
Definition 1.1[3] Let M be a linear space over F(
Summary
Introduction and PreliminariesThe notion of modular spaces was introduced by Nakano [1] in 1950 as a generalization of metric spaces and redefined and modified by Musielak and Ortiz [2] in 1959. Many results about fixed points in these spaces were considered such as [3,4,5,6]. Definition 1.1[3] Let M be a linear space over F( ). A function :M , - is called modular if (i) ( ) if and only if (ii) ( ) = ( ) for F with | | 1, for all M
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