CONE b-METRIC-LIKE SPACES OVER BANACH ALGEBRA AND FIXED POINT THEOREMS WITH APPLICATION

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Published: 2017-05-12

Page: 49-66


JEROLINA FERNANDEZ *

Department of Mathematics, NRI Institute of Information Science and Technology, Bhopal, 462021, M.P., India.

NEERAJ MALVIYA

Department of Mathematics, NRI Institute of Information Science and Technology, Bhopal, 462021, M.P., India.

SATISH SHUKLA

Department of Applied Mathematics, Shri Vaishnav Institute of Technology and Science, Gram Baroli Sanwer Road, Indore (M.P.) 453331, India.

*Author to whom correspondence should be addressed.


Abstract

The purpose of this article is to introduce a new generalization of the b-metric-like spaces called cone b-metric-like space over a Banach algebra A. Moreover, we discuss the topology generated by a cone b-metric-like space over Banach algebra . We also define generalized contraction mappings and expansive mappings in the new structure and prove some fixed point theorems for such mappings in the framework of cone b-metric-like space over Banach algebra. An example is also given to support the obtained results. Furthermore, we illustrate the application of our main results to the existence of solution of an integral equation. Our results extend, unify and generalize well known results of literature.

Keywords: Cone b-metric-like space over Banach algebra, c-sequence, generalized contractions, generalized expansive mapping, fixed point


How to Cite

FERNANDEZ, J., MALVIYA, N., & SHUKLA, S. (2017). CONE b-METRIC-LIKE SPACES OVER BANACH ALGEBRA AND FIXED POINT THEOREMS WITH APPLICATION. Asian Journal of Mathematics and Computer Research, 18(2), 49–66. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1014

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