Generalized Meir-Keeler type contractions and discontinuity at fixed point


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	Generalized Meir-Keeler type contractions and discontinuity at fixed point


	Fixed Point Theory, Volume 19, No. 1, 2018, 57-64, February 1st, 2018 DOI: 10.24193/fpt-ro.2018.1.06 Authors: Ravindra K. Bisht and Vladimir Rakočević Abstract: In this paper, we show that generalized Meir-Keeler type contractive definitions are strong enough to generate a fixed point but do not force the mapping to be continuous at the fixed point. Thus we provide more answers to the open question posed by B.E. Rhoades in the paper Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. Key Words and Phrases: Fixed point, (ε-δ) contractions, power contraction, orbital continuity. 2010 Mathematics Subject Classification: 47H09, 54E50, 47H10, 54E40. Published on-line: February 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents