New fixed point theorems for Ө-Φ contraction in complete metric spaces

In this paper, we introduce the notions of Ө-Φ contraction and Ө-Φ Suzuki contraction and establish some new fixed point theorems for these mappings in the setting of complete metric spaces. The results presented in the paper improve and extend the corresponding results due to Banach, Browder [F. E. Browder, Nederl. Akad. Wetensch. Proc. Ser. A Indag. Math., 30 (1968), 27–35], Suzuiki [T. Suzuki, Nonlinear Anal., 71 (2009), 5313–5317], Kannan [R. Kannan, Amer. Math. Monthly, 76 (1969), 405–408], Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages]. Finally, we give an example to illustrate them.