Fixed point theorems for quadruple self-mappings satisfying integral type inequalities

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In this paper, we study the generalization of (S,F)-rational contraction pair (h; 1) to almost (S,F,?)-rational contraction pair (h,g) of integral type on metric spaces. Further, we use the new generalized notion to produce some fixed point theorems via integral inequalities. This work generalizes many results in the available literature. For demonstration we give examples which show that our work generalizes many results.