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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. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

Content available
Article
Publication date: 22 February 2019

H. Fukhar-ud-din and A.R. Khan

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence…

Abstract

The purpose of this paper is to introduce the implicit midpoint rule (IMR) of nonexpansive mappings in 2- uniformly convex hyperbolic spaces and study its convergence. Strong and -convergence theorems based on this algorithm are proved in this new setting. The results obtained hold concurrently in uniformly convex Banach spaces, CAT(0) spaces and Hilbert spaces as special cases.

Details

Arab Journal of Mathematical Sciences, vol. 26 no. 1/2
Type: Research Article
ISSN: 1319-5166

Keywords

Content available
Article
Publication date: 9 February 2021

Godwin Amechi Okeke and Daniel Francis

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The…

Abstract

Purpose

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. The authors apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend generalize compliment and include several known results as special cases.

Design/methodology/approach

The results of this paper are theoretical and analytical in nature.

Findings

The authors prove the existence and uniqueness of fixed point of mappings satisfying Geraghty-type contractions in the setting of preordered modular G-metric spaces. apply the results in solving nonlinear Volterra-Fredholm-type integral equations. The results extend, generalize, compliment and include several known results as special cases.

Research limitations/implications

The results are theoretical and analytical.

Practical implications

The results were applied to solving nonlinear integral equations.

Social implications

The results has several social applications.

Originality/value

The results of this paper are new.

Details

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

Keywords

Content available
Article
Publication date: 5 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…

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. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

Content available
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…

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. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

Content available
Article
Publication date: 22 May 2019

Adrian Magdaş

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators…

Abstract

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

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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.

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