Riv. Mat. Univ. Parma, Vol. 6, No. 2, 2015

Satish Shukla[1]

Generalized Nadler $$G$$-contraction in cone metric spaces over Banach algebras endowed with a graph

Pages: 331-343
Received:7 September 2015
Accepted in revised form: 20 November 2015
Mathematics Subject Classification (2010): 47H10, 54H25.
Keywords:Cone metric space, set-valued mapping, Nadler $$G$$-contraction, fixed point.
Author address:
[1] : Department of Applied Mathematics, Shri Vaishnav Institute of Technology & Science , Gram Baroli, Sanwer Road, Indore, 453331, (M.P.) India

Abstract: In this paper, we introduce the generalized Nadler $$G$$-contractions in cone metric spaces endowed with a graph and defined over a Banach algebra. A fixed point result for such mappings is proved. Our result generalizes some known results in metric and cone metric spaces. An example is presented which verifies the significance and usability of the result proved herein.

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