Novel fixed point results for a class of enriched nonspreading mappings in real Banach spaces

Asima Razzaque; Imo Kalu Agwu; Naeem Saleem; Donatus Ikechi Igbokwe; Maggie Aphane; Asima Razzaque; Imo Kalu Agwu; Naeem Saleem; Donatus Ikechi Igbokwe; Maggie Aphane

doi:10.3934/math.2025181

AIMS Mathematics

2025, Volume 10, Issue 2: 3884-3909. doi: 10.3934/math.2025181

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Novel fixed point results for a class of enriched nonspreading mappings in real Banach spaces

1.
Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia
2.
Department of Mathematics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
3.
Department of Mathematics, Micheal Okpara University of Agriculture, Umudike, Umuahia Abia State, Nigeria
4.
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, Pretoria, 0204, South Africa

Received: 04 September 2024 Revised: 01 January 2025 Accepted: 14 January 2025 Published: 26 February 2025
MSC : 47H09, 47H10, 47J05, 65J15

A modified Halpern-type iterative technique, having weak and strong convergence results for approximating invariant points of a new class of enriched nonspreading operators subject to some standard mild conditions in the setting of real Banach spaces, was presented in this work. It was demonstrated with an example that the class of enriched nonspreading mappings includes the class of nonspreading mappings. Again, it was demonstrated with nontrivial examples that the class of enriched nonspreading mappings and the class of enriched nonexpansive mappings are independent. Some basic properties of the class of enriched nonspreading mappings were established. The results obtained solve the open question raised in Nonlinear Analysis 73 (2010): 1562–1568 for nonspreading-type mappings incorporating an averaged mapping. Moreover, we studied the estimation of common invariant points of this new class of mappings and the class of enriched nonexpansive operators and provided a strong convergence theorem for these mappings.
- variational inequality,
- enriched nonexpansive mapping,
- pseudocontractive,
- monotone mapping,
- Hilbert space,
- Lipschitizian,
- Banach space
Citation: Asima Razzaque, Imo Kalu Agwu, Naeem Saleem, Donatus Ikechi Igbokwe, Maggie Aphane. Novel fixed point results for a class of enriched nonspreading mappings in real Banach spaces[J]. AIMS Mathematics, 2025, 10(2): 3884-3909. doi: 10.3934/math.2025181

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Abstract

A modified Halpern-type iterative technique, having weak and strong convergence results for approximating invariant points of a new class of enriched nonspreading operators subject to some standard mild conditions in the setting of real Banach spaces, was presented in this work. It was demonstrated with an example that the class of enriched nonspreading mappings includes the class of nonspreading mappings. Again, it was demonstrated with nontrivial examples that the class of enriched nonspreading mappings and the class of enriched nonexpansive mappings are independent. Some basic properties of the class of enriched nonspreading mappings were established. The results obtained solve the open question raised in Nonlinear Analysis 73 (2010): 1562–1568 for nonspreading-type mappings incorporating an averaged mapping. Moreover, we studied the estimation of common invariant points of this new class of mappings and the class of enriched nonexpansive operators and provided a strong convergence theorem for these mappings.

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