Abstract
In this note, we introduce the notion of a generalized semi-quasi contraction and obtain a fixed point theorem for such contraction. Our results extend and generalize some well-known fixed point theorems including Ćirić’s quasi contraction theorem. As an application of our main theorem the existence of a solution for a class of functional equations arising in dynamic programming is discussed. At the end an open problem is also posed.
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We thank the referee for his valuable comments which lead substantially the improvement of the paper.
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Dedicated to my late father M. C. Pant
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Pant, R. Fixed point theorems for generalized semi-quasi contractions. J. Fixed Point Theory Appl. 19, 1581–1590 (2017). https://doi.org/10.1007/s11784-016-0308-x
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DOI: https://doi.org/10.1007/s11784-016-0308-x