Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces

Rajendra Pant,Rahul Shukla,Manuel De La Sen,Prashant Patel

doi:10.3390/sym13040585

Rajendra Pant, Rahul Shukla + Show 2 more

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https://doi.org/10.3390/sym13040585

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Abstract

In this paper, we present some fixed point results for a class of nonexpansive type and α-Krasnosel’skiĭ mappings. Moreover, we present some convergence results for one parameter nonexpansive type semigroups. Some non-trivial examples have been presented to illustrate facts.

Highlights

Introduction and PreliminariesSuppose Y is a nonempty subset of a Banach space X
Atailia et al [15] combined the SGNM and Hardy and Rogers [16] type nonexpansive mappings and introduced a new class of mappings called as generalized contractions of Suzuki type
If T : Y → Y is a generalized contraction of Suzuki type with β = 12 T is a generalized α–Reich–Suzuki nonexpansive mapping

Summary

Introduction and Preliminaries

Suppose Y is a nonempty subset of a Banach space X. In 2008, Suzuki [14] introduced a new class of nonexpansive type mappings known as mappings satisfying condition (C) and obtained some important fixed point results for these mappings. Atailia et al [15] combined the SGNM and Hardy and Rogers [16] type nonexpansive mappings and introduced a new class of mappings called as generalized contractions of Suzuki type They obtained some fixed point results for their new class of nonexpansive type mappings. We consider the Halpern iteration for finding a common fixed point of a nonexpansive type semigroup and a countable family of mappings satisfying condition (E) In this way, results in [5,15,17,18,19] have been extended, generalized and complimented.

Previous Results and Discussions

One Parameter Eμ Nonexpansive Semigroup

Conclusions