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Some fixed point results regarding convex contractions of Presić type

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Abstract

In the present paper, we introduce new types of Presić operators. These operators generalize the well-known Istrăţescu mappings, known as convex contractions. Also, we study the existence and uniqueness of fixed points for this type of operators and the convergence of one-step sequence toward the unique fixed point. Also, data dependence results are presented. Finally, some examples are given, suggesting that the above mappings are proper generalizations of convex contractions of second order.

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Acknowledgements

The author is thankful to Dr. Adrian Viorel from Technical University of Cluj-Napoca for important remarks and ideas that improved the present article. Last, but not least, the author is deeply indebted to the referees for valuable remarks that shaped the structure of this research article.

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Correspondence to Cristian Daniel Alecsa.

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Alecsa, C.D. Some fixed point results regarding convex contractions of Presić type. J. Fixed Point Theory Appl. 20, 7 (2018). https://doi.org/10.1007/s11784-018-0488-7

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  • DOI: https://doi.org/10.1007/s11784-018-0488-7

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