Some Iterations of Best Proximity Point

Authors

  • Jowan Hassan Mathematics Department, College of Science, University of Baghdad

DOI:

https://doi.org/10.31185/wjps.452

Keywords:

The best proximity point, Cyclic Kannan contraction mappings, Uniformly convex Banach space, Iterative sequences, Cyclic chatterjee contraction mapping.

Abstract

The aim of this paper is to investigate the convergence of two types of iterative methods , that is Manna and Ishikawa  to the optimal proximity points for cyclic Kannan and Chatterjee mappings defined on Banach spaces .

References

J. Z. Jamil and Z. Hussein, "Common fixed point of Jungck Picard iterative for two weakly compatible self-mappings," Iraqi J. Sci., vol. 62, no. 5, 2021.

A. Abkar and M. Gabeleh, "The existence of best proximity points for multivalued non-self-mappings," Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, vol. 107, pp. 319-325, 2013.

M. Jleli, E. Karapinar, and B. Samet, "Best proximity points for generalized α − ψ proximal contractive type mappings," [Online].

M. Jleli, E. Karapinar, and B. Samet, "A best proximity point result in modular spaces with the Fatou property," Abstr. Appl. Anal., 2013, 4 pages.

E. Karapinar, "Best proximity points of cyclic mappings," Appl. Math. Lett., vol. 25, pp. 1761-1766, 2012.

E. Karapinar, "Best proximity points of Kannan type cyclic weak Φ − contractions in ordered metric spaces," An. Științ. Univ. Ovidius Constanța Ser. Mat., vol. 20, pp. 51-63, 2012.

E. Karapinar, G. Petrusel, and K. Tas, "Best proximity point theorems for KT-types cyclic orbital contraction mappings," Fixed Point Theory, vol. 13, pp. 537-546, 2012.

S. Karpagam and S. Agrawal, "Best proximity point theorems for cyclic Meir-Keeler contraction maps," Nonlinear Anal., vol. 74, pp. 1040-1046, 2011.

C. Mongkolkeha and P. Kumam, "Best proximity point theorems for generalized cyclic contractions in ordered matrix spaces," J. Optim. Theory Appl., vol. 155, pp. 215-226, 2012.

H. K. Nashine, P. Kumam, and C. Vetro, "Best proximity point theorems for rational proximal contractions," Fixed Point Theory Appl., 2013, 11 pages.

V. S. Raj and P. Veeramani, "A best proximity theorems for weakly contractive non-self-mappings," Nonlinear Anal., vol. 74, pp. 4804-4808, 2011.

S. Basha, "Best proximity point theorems," J. Approx. Theory, vol. 163, pp. 1772-1781, 2011.

L. J. Khaleel and B. A. A. Ahmed, "Fixed point theorem for set valued mapping with rational condition," Iraqi J. Sci., vol. 61, no. 4, pp. 805-810, 2020.

K. A. Jassim and S. S. Abed, "Some results on best proximity in geodesic spaces," J. Phys. Conf. Ser., vol. 1804, no. 1, p. 012030, 2021.

Z. H. Maibed and S. S. Hussein, "Some theorems of fixed point approximations by iteration processes," J. Phys. Conf. Ser., vol. 1818, no. 1, p. 012153, 2021.

W. R. Mann, "Mean value methods in iteration," Proc. Am. Math. Soc., vol. 4, pp. 506-510, 1953.

S. Ishikawa, "Fixed points by a new iteration method," Proc. Am. Math. Soc., vol. 44, pp. 147-150, 1974.

E. Karapinar and I. M. Erhan, "Best proximity point on different type contractions," Appl. Math. Inf. Sci., vol. 5, no. 3, pp. 558-569, 2011.

A. A. Eldred and P. Veeramani, "Existence and convergence of best proximity points," J. Math. Appl., vol. 323, pp. 1001-1006, 2006.

A. Abkar and M. Gabeleh, "Global optimal solutions of non-cyclic mappings in metric spaces," J. Optim. Theory Appl., vol. 153, pp. 298-305, 2012.

S. Barootkoob, H. Lakzian, and Z. D. Mitrovic, "The best proximity points for weak MT-cyclic Reich type contractions," J. Math. Ext., vol. 16, no. 5, pp. 1-21, 2016.

M. A. Petric, "Best proximity point theorems for weak cyclic Kannan contractions," Filomat, vol. 25, no. 1, pp. 145-154, 2011.

A. Fernandez-Leon and M. Gabeleh, "Best proximity pair theorems for non-cyclic mappings in Banach and metric spaces," Fixed Point Theory, vol. 17, no. 1, pp. 63-84, 2016.

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Published

2024-09-30

Issue

Section

Mathematics

How to Cite

Hassan, J. (2024). Some Iterations of Best Proximity Point. Wasit Journal for Pure Sciences , 3(3), 50-57. https://doi.org/10.31185/wjps.452