Existence of Common Fixed Point for Pairs of Less-compatible Mappings of Type (E) in Symmetric Space


Published: 2023-03-10

Page: 141-149

Wakuma Masresha Kebede *

Department of Mathematics, Borana University, Oromia, Ethiopia.

Leta Bekere Kumssa

Department of Mathematics, Madda Walabu University, Oromia, Ethiopia.

*Author to whom correspondence should be addressed.


This paper presents a condition under which a common fixed point exist for pairs of self-mappings by defining new notions of less-compatibility of type (E) and α-generalized Ćirić type F- contraction. By these two notions we establish some common fixed point theorem and prove the Existence and uniqueness of common fixed point of mappings satisfying these notions. Generally, our study generalize and improve the result of Anita Tomar et al., “Electronic journal of mathematical analysis and application, Jan, 2019”. Additionally, different corollaries and some illustration is presented in our work.

Keywords: Common fixed point, compatible mapping of type (E), Ćirić type F- contraction

How to Cite

Kebede, W. M., & Kumssa, L. B. (2023). Existence of Common Fixed Point for Pairs of Less-compatible Mappings of Type (E) in Symmetric Space. Asian Journal of Advances in Research, 6(1), 141–149. Retrieved from https://mbimph.com/index.php/AJOAIR/article/view/3410


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Jungck G. Compatible mappings and fixed points. Internat. J. Math. Sci., 1986;9:381-390.

Sessa S. On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd). 1982;32:149-153.

Jungck G. Commuting mappings and fixed points. Amer. Math. Japon. 1976;38.

G. Jungck and B. E. Rhoades: Fixed point for set valued functions without continuity. Indian J. Pure Appl. Math. 1998;29(3):227-238.

Bouhadjera H, Thobie CG. Common fixed point theorems for pairs of sub compatible maps; 2009. arXiv0906.3159v1, 123-131.

Singh MR, Mahendra Singh Y. Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type. Internal J. Math. Sci. Engg. Appl. 2007;299-315.

Sriramula R, Srinavas V. Generation of a common fixed point theorem using A-Compatible and B- Compatible mappings of type (E). 2017;13:1735-1744

Wardowski D. Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl. 2012; 94:6.

Menac G, Helvac A, Altun I. Ćirić type generalized F-contractions on complete metric spaces and fixed point results. Filomat. 2014;28(6):1143-1151. DOI: 10.2298/FIL1406143M

Alshehri S, Arandelovic I, Shahzad N. Symmetric Spaces and Fixed Points of Generalized Contractions. 2014;Article ID 763547:8.

Tomar A, Sh. Updhayay and Ritu Sharma: Existence of fixed point in symmetric space with application. Electronic Journal of Mathematical Analysis and Application. 2019;7:116-129.

Beloul S. Common fixed point theorems for weakly sub sequentially continuous generalized contractions with applications. J. App. Math. E-notes. 2015;15:173-186.

Vetro P, Cosentino M. Fixed point results for F-contractive mappings of Hardy-Rogers type. Filomat. 2014;28(4):715– 722.

Tomar A, Ritu Sharma. Some coincidence and common fixed point theorems concerning f-contraction and applications. J. Internat. Math. Virtual Institute. 2018; 8:181-198. DOI: 10.7251/Jimvi1801181t.