AIMS Mathematics, 2020, 5(4): 3480-3494. doi: 10.3934/math.2020226

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Common fixed point results for couples $(f,g)$ and $(S,T)$ satisfy strong common limit range property

1 Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan
2 Department mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
3 Department of Medical Research, China Medical University, Taichung, Taiwan
4 Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

In this manuscript, we introduce strong common limit range property for couples $(f,g)$ and $(S, T)$ and by means of this new concept we establish common fixed point results for hybrid pair via $(F,\varphi)$-contraction and rational type contraction conditions. Further, we give some examples to support and illustrate our result. Using the established results existence of solution to the system of integral and differential equations are also discussed. We provide example where the main theorem is applicable but relevant classic result in literature fail to have a common fixed point.
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