# On Suzuki-Wardowski type fixed point theorems

Volume 8, Issue 6, pp 1095--1111
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### Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. Jamshaid Ahmad - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan. Akbar Azam - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.

### Abstract

Recently, Piri and Kumam [Fixed Point Theory and Applications 2014, 2014:210] improved concept of F- contraction and proved some Wardowski and Suzuki type fixed point results in metric spaces. The aim of this article is to define generalized $\alpha-GF$-contraction and establish Wardowski and Suzuki type fixed point results in metric and ordered metric spaces and derive main results of Piri et al. as corollaries. We also deduce certain fixed and periodic point results for orbitally continuous generalized F-contractions and certain fixed point results for integral inequalities are derived. Moreover, we discuss some illustrative examples to highlight the realized improvements.

### Share and Cite

##### ISRP Style

Nawab Hussain, Jamshaid Ahmad, Akbar Azam, On Suzuki-Wardowski type fixed point theorems, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 1095--1111

##### AMA Style

Hussain Nawab, Ahmad Jamshaid, Azam Akbar, On Suzuki-Wardowski type fixed point theorems. J. Nonlinear Sci. Appl. (2015); 8(6):1095--1111

##### Chicago/Turabian Style

Hussain, Nawab, Ahmad, Jamshaid, Azam, Akbar. "On Suzuki-Wardowski type fixed point theorems." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 1095--1111

### Keywords

• Fixed point
• $\alpha-GF$-contraction
• $\alpha-\eta$-continuous function
• orbitally continuous function.

•  47H10
•  54H25

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