Common fixed point results involving contractive condition of integral type in complex valued metric spaces

Volume 9, Issue 5, pp 2900--2913 http://dx.doi.org/10.22436/jnsa.009.05.84

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Authors

Mian Bahadur Zada - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan. Muhammad Sarwar - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan. Nasir Rahman - Department of mathematics and Statistics, Allam Iqbal open university, Islamabad, Pakistan. Muhammad Imdad - Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India.

Abstract

By using the Closed Range Property of the involved pairs (in short CLR property), common fixed point results for two pairs of weakly compatible mappings satisfying contractive condition of integral type in complex valued metric spaces are established, which are new even in ordinary metric spaces. We furnish suitable illustrative examples.

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Keywords

• Complex valued metric spaces
• common fixed points
• weakly compatible mappings
• (E:A) property
• (CLR) property.

MSC

•  47H10
•  54H25

References

• [1] M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188. , , , (),


• [2] M. Abbas, M. De la Sen, T. Nazir, Common fixed points of generalized cocyclic mappings in complex valued metric spaces, Discrete Dyn. Nat. Soc., 2015 (2015), 11 pages. , , , (),


• [3] J. Ahmad, N. Hussain, A. Azam, M. Arshad, Common fixed point results in complex valued metric space with applications to system of integral equations, J. Nonlinear Convex Anal., 16 (2015), 855-871., , , (),


• [4] [4] I. Altun, Common fixed point theorem for maps satisfying a general contractive condition of integral type, Acta Univ. Apulensis Math. Inform., 22 (2010), 195-206. , , , (),


• [5] I. Altun, D. Turkoglu, B. E. Rhoades, Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed Point Theory Appl., 2007 (2007), 9 pages., , , (),


• [6] [6] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), 243-253. , , , (),


• [7] S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math., 3 (1922), 133-181. , , , (),


• [8] [8] S. Bhatt, S. Chaukiyal, R. C. Dimri, A common fixed point theorem for weakly compatible maps in complex-valued metric spaces, Int. J. Math. Sci. Appl., 1 (2011), 1385-1389. , , , (),


• [9] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536., , , (),


• [10] [10] S. Chandok, D. Kumar, Some common fixed point results for rational type contraction mappings in complex valued metric spaces, J. Oper., 2013 (2013), 6 pages. , , , (),


• [11] A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329 (2007), 31-45. , , , (),


• [12] [12] N. Hussain, J. Ahmad, A. Azam, M. Arshad, Common fixed point results in complex valued metric spaces with application to integral equations, Filomat, 28 (2014), 1363-1380. , , , (),


• [13] G. Jungck, Common fixed points for non-continuous non-self mappings on a non-numeric spaces, Far East J. Math. Sci., 4 (1996), 199-212. , , , (),


• [14] [14] J. Kumar, Common fixed point theorems of weakly compatible maps satisfying (E.A.) and (CLR) property, Int. J. Pure Appl. Math., 88 (2013), 363-376. , , , (),


• [15] M. A. Kutbi, J. Ahmad, A. Azam, A. S. Al Rawashdeh, Generalized common fixed point results via greatest lower bound property, J. Appl. Math., 2014 (2014), 11 pages. , , , (),


• [16] [16] M. A. Kutbi, M. Arshad, J. Ahmad, A. Azam, Generalized common fixed point results with applications, Abstr. Appl. Anal., 2014 (2014), 7 pages. , , , (),


• [17] Z. Liu, Y. Han, S. M. Kang, J. S. Ume, Common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type, Fixed Point Theory Appl., 2014 (2014), 16 pages. , , , (),


• [18] [18] S. Manro, S. B. Jeong, S. M. Kang, Fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Anal., 7 (2013), 2811-2819. , , , (),


• [19] M. Mocanu, V. Popa, Some fixed point theorems for mappings satisfying implicit relations in symmetric spaces, Libertas Math., 28 (2008), 1-13., , , (),


• [20] [20] F. Rouzkard, M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl., 64 (2012), 1866-1874. , , , (),


• [21] M. Sarwar, M. Bahadur Zada, I. M. Erhan, Common fixed point theorems of integral type contraction on metric spaces and its applications to system of functional equations, Fixed Point Theory Appl., 2015 (2015), 15 pages. [, , , (),


• [22] 22] W. Sintunavarat, P. Kumam, Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J. Appl. Math., 2011 (2011), 14 pages. , , , (),


• [23] W. Sintunavarat, P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl., 2012 (2012), 12 pages. , , , (),


• [24] [24] R. K. Verma, H. K. Pathak, Common fixed point theorems using property (E.A) in complex-avlued metric spaces, Thai J. Math., 11 (2013), 347-355., , , (),