Tbilisi Mathematical Journal

$(\epsilon-\delta)$ conditions and fixed point theorems

Ravindra K. Bisht

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In this paper, we prove some fixed point theorems under generalized $(\epsilon-\delta)$ type rational contractions in which the fixed point may be a point of discontinuity. Our results generalize and improve a host of well-known fixed point theorems existing in the literature. In addition to it we give a fixed point theorem for $(\epsilon-\delta)$ non-expansive mappings in metric spaces. Several examples are given to illustrate our results.

Article information

Tbilisi Math. J., Volume 12, Issue 3 (2019), 39-49.

Received: 16 September 2018
Accepted: 22 June 2019
First available in Project Euclid: 26 September 2019

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Mathematical Reviews number (MathSciNet)

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
Secondary: 54E50: Complete metric spaces 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54E40: Special maps on metric spaces

fixed point $(\epsilon-\delta)$ condition non-expansive mapping discontinuous mappings $k$-continuity


Bisht, Ravindra K. $(\epsilon-\delta)$ conditions and fixed point theorems. Tbilisi Math. J. 12 (2019), no. 3, 39--49. doi:10.32513/tbilisi/1569463233. https://projecteuclid.org/euclid.tbilisi/1569463233

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