Document Type : Research Paper

Author

Department of Mathematics‎, ‎Faculty of Science and Arts‎, ‎Giresun University‎, ‎Turkey

Abstract

‎In this paper‎, ‎we introduce more general contractions called $\varphi$-fixed‎ ‎point point for $(F,\varphi‎ ,‎\alpha )_{s}$ and $(F,\varphi‎ ,‎\alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $\varphi$-‎fixed point point for $(F,\varphi‎ ,‎\alpha )_{s}$ and $(F,\varphi‎ ,‎\alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to support the usability of our results‎. ‎As applications‎, ‎necessary‎ ‎conditions to ensure the existence of a unique solution for a nonlinear‎ ‎inequality problem are also discussed‎. ‎Also‎, ‎some new fixed point results in‎ ‎partial metric spaces are proved.

Keywords

Main Subjects

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