C*-algebra valued partial metric space and some fixed point and coincidence point results

[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), 416–420.
[2] I. Altun and O. Acar, Fixed point theorems for weak contractions in the sense of berinde on partial metric spaces,
Topol. Appl. 159 (2012), 2642–2648.
[3] I. Altun, F. Sola, and H. Simsek, Generalized contractions on partial metric spaces, Topol. Appl. 157 (2010),
2778–2785.
[4] H. Aydi, M. Abbas, and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric
spaces, Topo. Appl. 159 (2012), 3234–3242.
[5] M. Bukatin, R. Kopperman, S. Matthews, and H. Pajoohesh, Partial metric spaces, Am. Math. Mon. 116 (2009),
708–718.
[6] L. Ciri´c, B. Samet, H. Aydi, and C. Vetro, Common fixed points of generalized contractions on partial metric
spaces and an application, Appl. Math. Comput. 218 (2011), 2398–2406.
[7] R. Douglas, Banach algebra techniques in operator theory, Springer, Berlin, 1998.
[8] R. H. Haghi, Sh. Rezapour, and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Analysis: Theory, Methods Appl. 74 (2011), 1799–1803.[9] R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures 7 (1999), 71–83.
[10] G. Jungck, Common fixed points for noncontinuous nonself maps on non-metric spaces, Far East J. Math. Sci. 4
(1996), 199–215.
[11] E. Karapinar and I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett. 24
(2011), 1894–1899.
[12] Z. Ma and L. Jiang, C
∗
-algebra-valued b-metric spaces and related fixed point theorems, Fixed Point Theory Appl.
2015 (2015), 2015:222.
[13] Z. Ma, L. Jiang, and H. Sun, C
∗
-algebra-valued metric spaces and related fixed point theorems, Fixed Point
Theory Appl. 2014 (2014), 2014:206.
[14] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. (1994), no. 728, 183–197.
[15] S. K. Mohanta, Common fixed points for mappings in G-cone metric spaces, J. Nonlinear Anal. Appl. 2012
(2012), doi:10.5899/ 2012/ jnaa-00120.
[16] , Common fixed point results in C ∗
-algebra valued b-metric spaces via digraphs, CUBO A Mathematical
Journal 20 (2018), 41–64.
[17] , Fixed points in C ∗
-algebra valued b-metric spaces endowed with a graph, Math. Slovaca 68 (2018),
639–654.
[18] G. Murphy, C
∗
-algebra and operator theory, Academic Press, London, 1990.
[19] H. K. Nashine and Z. Kadelburg, Cyclic contractions and fixed point results via control functions on partial metric
spaces, International J. Anal. (2013), Article ID 726387.
[20] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl.
(2010), Article ID 493298.
[21] M. P. Schellekens, The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci. 315
(2004), 135–149.