Hojat Ansari, A., Razani, A. (2017). Some fixed point theorems for $C$-class functions in $b$-metric spaces. Sahand Communications in Mathematical Analysis, (), -.

Arslan Hojat Ansari; Abdolrahman Razani. "Some fixed point theorems for $C$-class functions in $b$-metric spaces". Sahand Communications in Mathematical Analysis, , , 2017, -.

Hojat Ansari, A., Razani, A. (2017). 'Some fixed point theorems for $C$-class functions in $b$-metric spaces', Sahand Communications in Mathematical Analysis, (), pp. -.

Hojat Ansari, A., Razani, A. Some fixed point theorems for $C$-class functions in $b$-metric spaces. Sahand Communications in Mathematical Analysis, 2017; (): -.

Some fixed point theorems for $C$-class functions in $b$-metric spaces

Articles in Press, Accepted Manuscript , Available Online from 20 November 2017

^{1}Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

^{2}Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.

Abstract

In this paper, via $C$-class functions, as a new class of functions, a fixed theorem in complete $b$-metric spaces is presented. Moreover, we study some results, which are direct consequences of the main results. In addition, as an application, the existence of a solution of an integral equation is given.

[1] A. Aghajani, M. Abbas, and J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014) 941-960.

[2] A.H. Ansari, Note on φ-ψ-contractive type mappings and related fixed point, The 2nd regional conference on mathematics and applications, PNU, 2014, 377-380.

[3] A.H. Ansari, S. Chandok, and C. Ionescu, Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl., 2014:429 (2014) 17 pages.

[4] H. Aydi, M. Bota, E. Karapinar, and S. Mitrovic, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory Appl., 2012:88 (2012).

[5] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces (Russian), Func. An., Gos. Ped. Inst. Unianowsk, 30 (1989) 26-37.

[6] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Modern Math., 4(3) (2009) 285-301.

[7] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations int egrales, Fund. Math., 3 (1922) 133-181.

[8] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993) 5-11.

[9] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998) 263-276.

[10] Z.M. Fadail, A.G.B. Ahmad, A.H. Ansari, S. Radenovic, and M. Rajovic, Some common fixed point results of mappings in 0-σ-complete metric-like spaces via new function, Appl. Math. Sci., 9 (2015) no. 83 4109-4127.

[11] R.H. Haghi, Sh. Rezapour, and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011) 1799-1803.

[12] N. Hussain, V. Parvaneh, J.R. Roshan, and Z. Kadelburg, Fixed points of cyclic weakly (ψ, φ, L, A, B)-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013:256 (2013) 18 pages.

[13] M.S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30(1) (1984) 1-9.