### ∈φ-contraction and some fixed point results via modified ω-distance mappings in the frame of complete quasi metric spaces and applications

#### Abstract

In this Article, we introduce the notion of an ∈φ-contraction which based on modified ω-distance mappings and employ this new definition to prove some fixed point result. Moreover, we introduced an interesting example and an application to highlight the importance of our work.

#### Keywords

#### References

K. Abodayeh, W. Shatanawi, A. Bataihah, A.H. Ansari, Some xed point and common xed point results

through

distance under nonlinear contraction, Gazi University Journal of Science. 30:293-302, 2017.

K. Abodayeh, A. Batiahah, W. Shatanawi, Generalized

distance mappings and some xed point

theorems, Politehn Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys.,79 (2017), 223-232.

C. Alegre, J. Marin, Modied !-distance on quasi metric spaces and xed point theorems on complete

quasi metric spaces, Topol., Appl., 203 (2016), 120-129.

H. Aydi, M. Jellali, E. Karapnar, On xed point results for implicit contractions in quasi metric

spaces and consequences. Nonlinear Analysis Modelling and control. 2016, 21, 40{56.

H. Aydi, E. Karapinar, M. Postolache, Tripled coincidence point theorems for weak -contractions in

partially ordered metric spaces, Fixed Point Theory And Applications, 44 (2012).

H. Aydi, W. Shatanawi, M. Postolache, Z. Mustafa, and N. Tahat, Theorems for Boyd-Wong-Type

Contractions in Ordered Metric Spaces, Abstract and Applied Analysis, vol. 2012, Article ID 359054,

pages, (2012).

S. Banach, Sur les, Operation dans les ensembles abstraits et leur application aux equations integral,

Fundam. Math., 3:133-181, 1922.

N. Bilgili, E. Karapmar, B. Samet, Generalized quasi metric contractive mapping in quasi metric

spaces and related xed point theorems, J. Inequal. Appl., 2014:36,2014.

S. Chandok and M. Postolache, Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed

Point Theory and Applications vol 2013 (2013).

B.C. Dhage, Generalized metric spaces and mapping with xed point, Bulletin of the Calcutta Mathe-

matical Society, vol 84, no. 4, pp. 329-338.

M. Jleli, B. Samet, Remarks on G-metric spaces and xed point theorems, Fixed Point Theory Appl.,

: 210, 2012.

R. Kannan, Some results on xed point, Bull. Calcutta Math. Soi., 60 (1968), 71-76.

Z. Mustafa and B. Sims, Some remavles concerning D-metric spaces, in proceeding of the international

Conference on Fixed point theory and Applications, pp. 189-198 Vallencia, Spain.

I. Nuseir, W. Shatanawi, Issam Abu-Irwaq and Anwar Batiahah, Nonlinear contraction and xed point

theorems with modied !-distance mappings in complete quasi metric spaces, J. Nonlinear Sci. Appl.,

(2017), 5342-5350.

T. Qawasmeh, W. Shatanawi, A. Bataihah and A. Tallafha Common Fixed Point Results for Rational

(; )'-m! Contractions in Complete Quasi Metric Spaces, Mathematics, 2019 (7), 392.

T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc.

Amer. Math. Soc., 136 (2008), 1861-1869.

W. Shatanawi, M. Postolache, Coincidence and xed point results for generalized weak contractions in

the sense of Berinde on partial metric spaces, Fixed Point Theory and Applications, vol 2013 (2013).

W. Shatanawi, M. Postolache, Common xed point results for mappings under nonlinear contraction of

cyclic form in ordered metric spaces, Fixed Point Theory and Applications, vol. 2013. (2013).

W. Shatanawi, Fixed and common xed point theoerms in frame of quasi metric spaces based on ultra

distance functions, Nonlinear Analysis: Modelling and Control, 2018, Vol. 23, No. 5, 724{748.

W. Shatanawi, M.S. Noorani, H. Alsamir, A. Bataihah, Fixed and common xed point theorems in

partially ordered quasi metric spaces, J. Math. Computer Sci. 16:516-528, 2012.

W. Shatanawi, A. Pitea, Some coupled xed point theorems in quasi-partial metric spaces,Fixed Point

DOI: http://doi.org/10.11591/ijece.v10i4.pp%25p

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.