Hardy-Rogers-type fixed point theorems for $\alpha $-$GF$-contractions

Muhammad Arshad, Eskandar Ameer, and Aftab Hussain

Address: Department of Mathematics, International Islamic University, H-10, Islamabad - 44000, Pakistan


Abstract: The aim of this paper is to introduce some new fixed point results of Hardy-Rogers-type for $\alpha $-$\eta $-$GF$-contraction in a complete metric space. We extend the concept of $F$-contraction into an $\alpha $-$\eta $-$GF$-contraction of Hardy-Rogers-type. An example has been constructed to demonstrate the novelty of our results.

AMSclassification: primary 46S40; secondary 47H10, 54H25.

Keywords: metric space, fixed point, $F$-contraction, $\alpha$-$\eta$-$GF$-contraction of Hardy-Rogers-type.

DOI: 10.5817/AM2015-3-129