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Open Access
Article
Publication date: 5 March 2021

Julee Srivastava

In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard…

Abstract

Purpose

In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid and Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

Design/methodology/approach

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings.

Findings

Showed the fastest convergence of this new iteration and then other iteration defined in this paper. The author finds the solution of delay differential equation using this hybrid iteration. For new iteration, the author also proved a theorem for nonexpansive mapping.

Originality/value

This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative processes for contraction mappings and to find the solution of delay differential equation, using this hybrid iteration also proved some results for Picard–S hybrid iterative process for nonexpansive mappings.

Details

Arab Journal of Mathematical Sciences, vol. 28 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Open Access
Article
Publication date: 4 January 2021

Sushanta Kumar Mohanta

In this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of…

Abstract

Purpose

In this paper, we use the notion of cyclic representation of a nonempty set with respect to a pair of mappings to obtain coincidence points and common fixed points for a pair of self-mappings satisfying some generalized contraction- type conditions involving a control function in partial metric spaces. Moreover, we provide some examples to analyze and illustrate our main results.

Design/methodology/approach

Theoretical method.

Findings

We establish some coincidence points and common fixed point results in partial metric spaces.

Originality/value

Results of this study are new and interesting.

Details

Arab Journal of Mathematical Sciences, vol. 27 no. 2
Type: Research Article
ISSN: 1319-5166

Keywords

Open Access
Article
Publication date: 8 February 2019

Godwin Amechi Okeke and Safeer Hussain Khan

The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued

Abstract

The purpose of this paper is to extend the recent results of Okeke et al. (2018) to the class of multivalued ρ-quasi-contractive mappings in modular function spaces. We approximate fixed points of this class of nonlinear multivalued mappings in modular function spaces. Moreover, we extend the concepts of T-stability, almost T-stability and summably almost T-stability to modular function spaces and give some results.

Open Access
Article
Publication date: 13 January 2021

Hudson Akewe and Hallowed Olaoluwa

In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to…

Abstract

Purpose

In this paper, the explicit multistep, explicit multistep-SP and implicit multistep iterative sequences are introduced in the context of modular function spaces and proven to converge to the fixed point of a multivalued map T such that PρT, an associate multivalued map, is a ρ-contractive-like mapping.

Design/methodology/approach

The concepts of relative ρ-stability and weak ρ-stability are introduced, and conditions in which these multistep iterations are relatively ρ-stable, weakly ρ-stable and ρ-stable are established for the newly introduced strong ρ-quasi-contractive-like class of maps.

Findings

Noor type, Ishikawa type and Mann type iterative sequences are deduced as corollaries in this study.

Originality/value

The results obtained in this work are complementary to those proved in normed and metric spaces in the literature.

Details

Arab Journal of Mathematical Sciences, vol. 27 no. 2
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 1 January 1980

WINFRIED GÖDERT

In this paper we will try to reach a twofold goal. First we will give an analysis of mathematical terminology in order to give practical hints for assigning subject headings to a…

Abstract

In this paper we will try to reach a twofold goal. First we will give an analysis of mathematical terminology in order to give practical hints for assigning subject headings to a book. Secondly, we will propose a method which could be helpful for the subject analysis of a given document. The main basis for this method is the connection between a special classification scheme, the Subject Classification Scheme of the American Mathematical Society, and the task of indexing books by subject headings. Examples of this method are given, and they are compared with Library of Congress Subject Headings and PRECIS entries. With both the study of the terminology and the proposed method, it should be possible to increase quality and consistency of the library indexing results for mathematical books. A thesaurus for mathematics with entries along the lines of the PRECIS rules and connected with the subject classification scheme of the American Mathematical Society, would be desirable, as would the printing of appropriate classification data, assigned to them by their authors, inside the books.

Details

Journal of Documentation, vol. 36 no. 1
Type: Research Article
ISSN: 0022-0418

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