$(F,\varphi ,\alpha )_{s}$-contractions in $b$-metric spaces and applications
محورهای موضوعی : Fixed point theory
1 - Department of Mathematics, Faculty of Science and Arts, Giresun University, Turkey
کلید واژه: $b$-metric space, &lrm, partial $b$-metric space&lrm, , $(F, varphi, alpha )_{s}$-contraction, $varphi$-fixed point,
چکیده مقاله :
In this paper, we introduce more general contractions called $\varphi $-fixedpoint 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 aresupplied to support the usability of our results. As applications, necessaryconditions to ensure the existence of a unique solution for a nonlinearinequality problem are also discussed. Also, some new fixed point results inpartial metric spaces are proved.
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