Document Type: Special Issue on Fixed Point Theory

Authors

1 Department of Humanities and Basics Sciences, School of Engineering, Matoshri Pratishthan Group of Institutions, Nanded, India

2 University of Banja Luka, Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina

3 School of Mathematical Sciences, Swami Ramanandh Teerth Marathwada University, Nanded, India

Abstract

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. and Engg. Appl. (6) (2012), 129-136].

Keywords

Main Subjects

[1] S. Banach, Sure les operations dans les ensembles abstraits et leur applicaiton aux equations integrales, Fund. Math. 3 (1922), 133-181.

[2] H. Liu, S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl. 320 (2013), 1-10.

[3] Z. D. Mitrovic, On an open problem in rectangular b-metric space, J. Anal. 25 (1) (2017), 135-137.

[4] K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. Math. Sci. and Engg. Appl. 6 (2012), 129-136.

[5] S. Xu, S. Radenovi´c, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebra without assumption of normality, Fixed Point Theory Appl. 102 (2014), 1-12.

[6] S. Radenovic, B. E. Rhoades, Fixed point theorems for two non-self mappings in cone metric spaces, Comput. Math. Appl. 57 (2009), 1701-1707.

[7] H. Huang, S. Radenovi´c, Some fixed point results of generalized Lipschitz mappings on cone b-metric spaces over banach algebra, J. Comput. Anal. Appl. 20 (2016), 566-583.