Abstract
In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.
Funding source: National Research Foundation
Award Identifier / Grant number: 119903
Funding statement: The second author is supported by the Department of Science and Innovation (DSI) and National Research Foundation (NRF), Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903).
Acknowledgements
The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS or NRF.
Competing Interests: The authors declare that they have no competing interests.
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Articles in the same Issue
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations