EXISTENCE AND STABILITY RESULTS FOR COINCIDENCE POINTS OF NONLINEAR CONTRACTIONS

Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu

DOI Number
10.22190/FUMI1704469C
First page
469
Last page
483

Abstract


In this paper we define $\alpha$ - admissibility of multi-valued mapping with respect to a single-valued mapping and use this concept to establish a coincidence point theorem for pairs of nonlinear multi-valued and single-valued mappings under the assumption of an inequality with rational terms. We illustrate the result with an example. In the second part of the paper we prove the stability of the coincidence point sets associated with the pairs of mappings in our coincidence point theorem. For that purpose we define the corresponding stability concepts of coincidence points. The results are primarily in the domain of nonlinear set-valued analysis.

Keywords

Hausdorff metric, $\alpha$-admissible mappings, coincidence point, stability

Keywords


Hausdorff metric; $\alpha$-admissible mappings; coincidence point; stability.

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References


P. Amiri, Sh. Rezapour, N. Shahzad, Fixed points of generalized $alpha$ − $psi$ - contractions, RACSAM 108 (2) (2014), 519–526.

S. Banach, Sur les oprations dans les ensembles abstraits et leurs applications aux quations intgrales, Fund Math. 3(1922), 133–181.

C. D. Bari, C. Vetro, Common fixed point theorems for weakly compatible maps satisfying a general contractive condition, Int. J. Math. Math. Sci. 2008 (2008), Article ID 891375.

G. V. R. Babu, K. N. V. V. Vara Prasad, Common fixed point theorems of different compatible type mappings using Ćirić’s contraction type condition, Math. Commun. 11 (2006), 87-102.

R. K. Bose, R. N. Mukherjee, Stability of fixed point sets and common fixed points of families of mappings, Indian J. Pure Appl. Math. 9 (1980), 1130–1138.

B. S. Choudhury, N. Metiya, Coincidence point theorems for a family of multivalued mappings in partially ordered metric spaces, Acta Universitatis Matthiae Belii, series Mathematics 21 (2013), 13–26.

B. S. Choudhury, N. Metiya, M. Postolache, A generalized weak contraction principle with applications to coupled coincidence point problems, Fixed Point Theory Appl. 2013 (2013) : 152.

B. S. Choudhury, N. Metiya, C. Bandyopadhyay, Fixed points of multivalued -admissible mappings and stability of fixed point sets in metric spaces, Rend. Circ. Mat. Palermo 64 (2015), 43–55.

B. S. Choudhury, N. Metiya, T. Som, C. Bandyopadhyay, Multivalued fixed point results and stability of fixed point sets in metric spaces, Facta Universitatis (NIŠ) Ser. Math. Inform. 30 (4) (2015), 501–512.

N. Hussain, E. Karapinar, P. Salimi, F. Akbar, $alpha$-admissible mappings and related fixed point theorems, Journal of Inequalities and Applications 2013 (2013) : 114.

G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771-779.

S. M. Kang, Y. J. Cho, G. Jungck, Common fixed point of compatible mappings, Int. J. Math. Math. Sci. 13 (1990), 61-66.

E. Karapinar, B. Samet, Generalized − contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), Article ID 793486.

T. C. Lim, Fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985), 436–441.

J. T. Markin, A fixed point stability theorem for nonexpansive set valued mappings, J. Math. Anal. Appl. 54 (1976), 441–443.

S. B. Nadler Jr., Sequences of contractions and fixed points, Pacifc J. Math. 27 (1968), 579–585.

S. B. Jr. Nadler, Multivalued contraction mapping, Pac. J. Math. 30 (1969), 475–488.

A. Razani, M. Yazdi, Two common fixed point theorems for compatible mappings, Int. J. Nonlinear Anal. Appl. 3 (2010), 22-33.

B. Samet, C. Vetro, P. Vetro, Fixed point theorems for $alpha$ − $psi$ -contractive type mappings, Nonlinear Anal. 75 (2012), 2154–2165.

P. Salimi, A. Latif, N. Hussain, Modified $alpha$ − $psi$ - contractive mappings with applications, Fixed Point Theory Appl. 2013 (2013) : 151.

D. Türkoğlu, O. Özer, B. Fisher, A coincidence point theorem for multivalued contractions, Math. Commun. 7(2002), 39–44.




DOI: https://doi.org/10.22190/FUMI1704469C

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