## Tbilisi Mathematical Journal

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

Ravindra K. Bisht

#### Abstract

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

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

Dates
Accepted: 22 June 2019
First available in Project Euclid: 26 September 2019

https://projecteuclid.org/euclid.tbilisi/1569463233

Digital Object Identifier
doi:10.32513/tbilisi/1569463233

Mathematical Reviews number (MathSciNet)
MR4012382

#### Citation

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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