Details

V. H. Badshah ^[a], Prakash Bhagat ^[b] and Satish Shukla ^[c]

Some fixed point theorems for generalized \(\mathcal{R}\)-Lipschitz mappings in linear cone \(2\)-normed spaces

Pages: 193-209
Received: 11 May 2016
Accepted in revised form: 25 September 2017
Mathematics Subject Classification (2010): 47H10; 54H25.
Keywords: Cone \(2\)-normed space, binary relation, generalized \(\mathcal{R}\)-Lipschitz mapping, fixed point.
Author address:
[a]: School of Studies in Mathematics, Vikram University, Ujjain, (M.P.), India
[b]: Department of Applied Mathematics, NMIMS, MPSTME, Shirpur, India
[c]: 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 concept of linear cone \(2\)-normed spaces and prove some fixed point results for generalized \(\mathcal{R}\)-Lipschitz contractions in linear cone \(2\)-normed spaces endowed with a binary relation \(\mathcal{R}\). We observe that the fixed point of the considered mappings can be approximated with Mann iteration scheme. Our results generalize and extend several known results of literature into linear cone \(2\)-normed spaces. Some examples are provided which illustrate the new concepts and the results.

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