SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FORα-GF-CONTRACTIONS

Recently, Wardowski [Fixed Point Theory Appl. 2012:94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. Abbas et al. [2] further generalized the concept of F-contraction and proved certain fixed...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 18; no. 6; pp. 1879 - 1895
Main Authors Hussain, N., Salimi, P.
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2014
Subjects
Continuous functions
Diagonal lemma
Mathematical functions
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Summary:Recently, Wardowski [Fixed Point Theory Appl. 2012:94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. Abbas et al. [2] further generalized the concept of F-contraction and proved certain fixed and common fixed point results. In this paper, we introduce anα-GF-contraction with respect to a general family of functionsGand establish Wardowski type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki type fixed point results for GF-contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized F-contractions. Moreover, we discuss some illustrative examples to highlight the realized improvements. 2010Mathematics Subject Classification: 46N40, 47H10, 54H25, 46T99. Key words and phrases: Fixed point,α-GF-contraction,α-η-Continous function, Orbitally continuous function.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.18.2014.4462