Approximate Solution of a Nonlinear Volterra–Fredholm Integral Equations Via New 𝒵-Iterative Algorithm
Salman Zaheer
Department of Mathematics, Vellore Institute of Technology, Vellore, India
Contribution: Software, Investigation, Writing - original draft, Methodology, Validation, Formal analysis
Search for more papers by this authorCorresponding Author
Ankush Chanda
Department of Mathematics, Vellore Institute of Technology, Vellore, India
Correspondence:
Ankush Chanda ([email protected])
Hemant Kumar Nashine ([email protected])
Contribution: Conceptualization, Writing - review & editing, Validation, Software, Supervision
Search for more papers by this authorCorresponding Author
Hemant Kumar Nashine
Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Sehore, Madhya Pradesh, India
Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa
Correspondence:
Ankush Chanda ([email protected])
Hemant Kumar Nashine ([email protected])
Contribution: Validation, Writing - review & editing, Software, Supervision, Resources
Search for more papers by this authorSalman Zaheer
Department of Mathematics, Vellore Institute of Technology, Vellore, India
Contribution: Software, Investigation, Writing - original draft, Methodology, Validation, Formal analysis
Search for more papers by this authorCorresponding Author
Ankush Chanda
Department of Mathematics, Vellore Institute of Technology, Vellore, India
Correspondence:
Ankush Chanda ([email protected])
Hemant Kumar Nashine ([email protected])
Contribution: Conceptualization, Writing - review & editing, Validation, Software, Supervision
Search for more papers by this authorCorresponding Author
Hemant Kumar Nashine
Mathematics Division, School of Advanced Sciences and Languages, VIT Bhopal University, Sehore, Madhya Pradesh, India
Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa
Correspondence:
Ankush Chanda ([email protected])
Hemant Kumar Nashine ([email protected])
Contribution: Validation, Writing - review & editing, Software, Supervision, Resources
Search for more papers by this authorABSTRACT
In this paper, we pay attention to explore the existence of common fixed points of a pair of - nonexpansive mappings. To execute the objective, firstly, we propose a novel three step iterative algorithm, namely -iteration, for a pair of mappings. Furthermore, we enquire for a few weak and strong convergence results and endorse the existence of common fixed points for two - nonexpansive mappings. Our results are validated by constructive numerical examples. Lastly, the newly proposed iterative algorithm is employed to approximate the solution of a certain type of nonlinear Volterra–Fredholm integral equations on Banach spaces. Furthermore, an example on integral equations is constructed to authenticate our finding.
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