Shojaei, H., Shojaei, N., Mortazaei, R. (2019). Common Fixed Point in Cone Metric Space for $\mathbf{s}-\mathbf{\varphi}$-contractive. Sahand Communications in Mathematical Analysis, 14(1), 15-26. doi: 10.22130/scma.2018.65773.251

Hamid Shojaei; Neda Shojaei; Razieh Mortazaei. "Common Fixed Point in Cone Metric Space for $\mathbf{s}-\mathbf{\varphi}$-contractive". Sahand Communications in Mathematical Analysis, 14, 1, 2019, 15-26. doi: 10.22130/scma.2018.65773.251

Shojaei, H., Shojaei, N., Mortazaei, R. (2019). 'Common Fixed Point in Cone Metric Space for $\mathbf{s}-\mathbf{\varphi}$-contractive', Sahand Communications in Mathematical Analysis, 14(1), pp. 15-26. doi: 10.22130/scma.2018.65773.251

Shojaei, H., Shojaei, N., Mortazaei, R. Common Fixed Point in Cone Metric Space for $\mathbf{s}-\mathbf{\varphi}$-contractive. Sahand Communications in Mathematical Analysis, 2019; 14(1): 15-26. doi: 10.22130/scma.2018.65773.251

Common Fixed Point in Cone Metric Space for $\mathbf{s}-\mathbf{\varphi}$-contractive

^{1}Department of Mathematics, Afzale Kermani, Institute of Higher Education,, Kerman, Iran.

^{2}Department of Mathematics, Afzale Kermani, Institute of Higher Education, Kerman, Iran.

^{3}Department of Mathematics, Afzale Kermani Institute of Higher Education, Kerman, Iran.

Abstract

Huang and Zhang \cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei \cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space. In this paper, the notion of complete cone metric space has been introduced. We have defined $s-\phi$-contractive and obtained common fixed point theorem for a mapping $f,s$ which satisfies $s-\phi$-contractive.

[1] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), pp. 416-420.

[2] D.W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), pp. 458-464.

[3] C. Di Bari and P. Vetro, $phi$-pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 57 (2008), pp. 279-285.

[4] L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), pp. 1468-1476.

[5] D. Ilic and C.V. Rakocevi, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), pp. 876-882.

[6] E. Karapinar, Fixed point theory for cyclic $phi$-contractions, Appl. Math. Lett, 24 (2011), pp. 822-825.

[7] W.A. Kirk, P.S. Srinivasan, and P. veeramany, Fixed point theorem for mapping satisfying cycle contractive condition, Fixed point theory, 4 (2003), pp. 79-89.

[8] R.P. Pant, Common fixed points for contractive maps, J. Math. Anal. Appl. 226 (1998), pp. 251-251.

[9] H. Shojaei, Some Theorem for Common Fixed Point for S-Contraction Mappings in Complete Cone Metric Spaces, International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC), 5 (2017), pp. 241-251.

[10] H. Shojaei and R. Mortezaei, Common Fixed Point for Affine Self Maps Invariant Approximation in p-normed Spaces, J. Math. Computer Sci., 6 (2013), pp. 201-209.

[11] D. Turkoglu, Cone metric spaces and fixed diametrically contractive mapping, Acta Math. Sin. (Engl. Ser.), 26 (2010), pp. 489-496.

[12] P. Vetro, Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo (2), 56 (2007), pp. 464-468.