Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process

Piri, Hossein; Daraby, Bayaz; Rahrovi, Samira; Ghasemi, Mostafa

doi:10.1007/s11075-018-0588-x

Cited by 22 publications

(17 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Picard Ishikawa type iteration process was introduced by Piri et al [34]. They claimed that this iterative process converges faster than Mann and Ishikawa iteration processes.…”

Section: Definition 2 ([6]mentioning

confidence: 99%

Generation of Julia and Mandelbrot Sets via Fixed Points

2020

View full text Add to dashboard Cite

The aim of this paper is to present an application of a fixed point iterative process in generation of fractals namely Julia and Mandelbrot sets for the complex polynomials of the form T ( x ) = x n + m x + r where m , r ∈ C and n ≥ 2 . Fractals represent the phenomena of expanding or unfolding symmetries which exhibit similar patterns displayed at every scale. We prove some escape time results for the generation of Julia and Madelbrot sets using a Picard Ishikawa type iterative process. A visualization of the Julia and Mandelbrot sets for certain complex polynomials is presented and their graphical behaviour is examined. We also discuss the effects of parameters on the color variation and shape of fractals.

show abstract

“…The Picard Ishikawa type iteration process was introduced by Piri et al [34]. They claimed that this iterative process converges faster than Mann and Ishikawa iteration processes.…”

Section: Definition 2 ([6]mentioning

confidence: 99%

Generation of Julia and Mandelbrot Sets via Fixed Points

2020

View full text Add to dashboard Cite

show abstract

“…The following lemma recalls some basic properties of the (α, β)-Suzuki mappings as they were stated and proved in [13] for properly chosen parameters (we shall refer to such convenient parameters as admissible parameters).…”

Section: Definition 2 (Seementioning

confidence: 99%

“…• In [13], the class of Suzuki-type generalized nonexpansive mappings on Banach spaces was changed in connection with an admissible pair of parameters. This new property extends Suzuki's condition, but remains subordinated to quasinonexpansiveness.…”

Section: Introductionmentioning

confidence: 99%

“…• Condition (C) in [4] as a modular extension of the Suzuki's nonexpansiveness property; • The modular Suzuki-type generalized nonexpansive mappings in [3] as a modular extension for the mappings defined in [13], as well as generalization for mappings satisfying condition (ρC); • Condition (ρE) in [8], i.e. the modular version of condition (E).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A unifying approach for some nonexpansiveness conditions on modular vector spaces

Bejenaru

Postolache

2020

NAMC

View full text Add to dashboard Cite

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

show abstract

“…The Mann [20] iterative scheme has been used to study the approximation of fixed points of nonexpansive mappings by many authors [21][22][23][24][25][26]. Following the same line, we define the Mann process in the framework of hyperbolic metric spaces in order to prove its convergence to fixed points for monotone mapping satisfying condition B γ,μ .…”

Section: Journal Of Function Spacesmentioning

confidence: 99%