Continuity and Fixed Point of a new extension of $F$-Suzuki-Contraction Mappings in b-metric Spaces with Application

Authors

  • Zahra Ahmadi
  • Rahmatollah Lashkaripour
  • Hamid Baghani

DOI:

https://doi.org/10.30495/jme.v14i0.1041

Keywords:

Fixed point, Continuity, SO-b-complete, $F_{p}$-Suzuki-Contraction mapping

Abstract

In this paper, firstly, we introduce a new extension of F-Suzuki-contraction mappings namely generalized $F_p$-Suzuki contraction. Moreover, we prove a fixed point theorem for such contraction mappings even without considering the completeness condition of space. In the following, we respond the open question of Rhoades(see Rhoades \cite{23}, p.242) regarding existence of a contractive definition which is strong enough to generate a fixed point but dose not force the mapping to be continuous at the fixed point.  Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value problem of a nonlinear fractional differential equation for our results.

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Published

2019-09-22

Issue

Vol. 14

Section

Vol. 14, No. 4, (2020)

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