Some ? -Fixed Point Results for ( F, ?, ? - ? )-Contractive Type Mappings with Applications

Mohammad Imdad, Abdur Rauf Khan, Hayel N. Saleh and Waleed M. Alfaqih
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Mohammad Imdad: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Abdur Rauf Khan: Department of Applied Sciences, University Polytechnic, Aligarh Muslim University, Aligarh 202002, India
Hayel N. Saleh: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Waleed M. Alfaqih: Department of Mathematics, Hajjah University, Hajjah 1729, Yemen

Mathematics, 2019, vol. 7, issue 2, 1-16

Abstract: In this paper, we introduce the notions of ( F , φ , α - ψ )-contractions and ( F , φ , α - ψ )-weak contractions in metric spaces and utilize the same to prove some existence and uniqueness φ -fixed point results. Some illustrative examples are given to demonstrate the usefulness and effectiveness of our results. As applications, we deduce some fixed point theorems in partial metric spaces besides proving an existence result on the solution of nonlinear differential equations. Our results extend, generalize and improve some relevant results of the existing literature.

Keywords: ? -fixed point; ? - ? -contraction mappings; ( F , ? , ? - ? )-contraction mappings; ( F , ? , ? - ? )-weak contraction mappings; partial metric spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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